All right, I've finally watched the episode. I'll start adding what I've found and stuff people have commented now. Thanks for commenting! Please bear with the changes while I update the post. Please feel free to continue commenting if you find anything else, however please read the post and other comments before commenting to avoid posting the same information. Thanks!
"Vincent van Gogh!" (0:20)
Vincent van Gogh (ヴィンセント・ヴァン・ゴッホ) is the name of a Dutch impressionist painter.S1
"Judekka Gohho!" (0:27)
"Judekka Gohho" (ジュデッカゴッホ) is referencing a character named Judekka Gottsuo (ジュデッカ・ゴッツォ) from "Suupaa Robotto Taisen" (スーパーロボット大戦), "Super Robot Wars", a video game series that first began release in 1991.S1
"In the first place, why can an alien catch a cold?" (0:44)
"We don't have immunity to viruses on Earth." (0:47)
This is referencing "The War of the Worlds", a novel written by H. G. Wells and published in 1898.S2 In the novel, Martians weilding overwhelming technological power invade Earth, however they eventually die off due to lack of immunity to bacteria on Earth. As stated in the novel, the Martians were "slain by the putrefactive and disease bacteria against which their systems were unprepared". It is further stated, "But there are no bacteria in Mars, and directly these invaders arrived, directly they drank and fed, our microscopic allies began to work their overthrow."
"Even aliens possessing overwhelming power can have surprising weaknesses, like tomatoes, moon rocks, or music." (1:05)
There are three references here:
* Weakness to tomatoes is referencing "Daijoubu Mai Furendo" (だいじょうぶマイフレンド), "It's All Right My Friend", a Japanese movie released in 1983.S2 The main character of the movie, Gonjii Toroimerai (ゴンジー・トロイメライ), is an alien with super human power and a weakness to tomatoes. Being near tomatoes makes him weaker.
* Weakness to moon rocks is referencing "Uchuu Daikaijuu Girara" (宇宙大怪獣ギララ), "Giant Space Monster Girara", a Japanese movie released in 1967.S1 In the movie, there is a giant monster from space called Girara that possesses overwhelming power and grows larger and more powerful by absorbing energy. It goes on a rampage on Earth in search of more energy, and all weapons are unable to damage it. Eventually, a substance called Giraraniumu (ギララニウム) is discovered, which is able to block energy absorption and radiation. It is also discovered that Giraraniumu is abundantly found in moon rocks. Girara is defeated by bombs full of moon rocks that cover Girara in Giraranium and cause it to weaken and shrink. The image that appears on screen when Nyaruko mentions weakness to moon rocks contains a silhouette of a space ship used in the movie called "AAB Ganmaa Gou" (AABガンマー号), "AAB Gamma Model". The image also contains a silhouette of Girara. Images for reference:
Source of image: http://en.wikipedia.org/wiki/File:The-X-from-Outer-Space.jpg
* Weakness to music is referencing "Mars Attacks!", an American movie released in 1996.S1 In the movie, Martians weilding overwhelming technological power invade Earth, however it is eventually revealed that the heads of the Martians explode due to hearing the song "Indian Love Call" sung by Slim Whitman. The image that appears on screen when Nyaruko mentions weakness to music contains silhouettes of Martians as they appear in "Mars Attacks!". Images for reference:
"Achoo Great Evil God!" (1:27)
The Japanese line is "Hakushon Daijashin!" (ハクション大邪神！). "Hakushon" (ハクション) is the Japanese interpretation of the sound made when someone sneezes. As a whole, "Hakushon Daijashin" is referencing "Hakushon Daimaou" (ハクション大魔王), "Achoo Great Demon King", an anime series that aired from 1969 to 1970.S1 The series is about a genie named Hakushon Daimaou (ハクション大魔王) who is summoned from his pot when someone sneezes.
"We're going to make a heartbeat memorial." (1:42)
"Tokimeki na memoriaru" (ときめきなメモリアル), "heartbeat memorial", is referencing "Tokimeki Memoriaru" (ときめきメモリアル), "Heartbeat Memorial", a video game released in 1994.S2
"I'm going to confess to the boy under the sakura tree that never withers." (2:34)
"Karenai sakura no hi" (枯れない桜の木), "sakura tree that never withers", is referencing "D.C. ~Da Capo~" (D.C. ～ダ・カーポ～), a visual novel released by CIRCUS in 2002.S2 In the story there is a "karenai sakura" (枯れない桜), "sakura tree that never withers".
"Fan disc!" (2:43)
"Fan disuku" (ファンディスク), "fan disc", is an item released by a game company as a follow up to a previous game. A fan disc typically contains bonus material related to the original game.S2
The title of this episode is "Yugosu Atakku!" (ユゴス・アタック！), which translates to "Yuggoth Attack!". There are two references here:
* This is referencing "Mars Attacks!", an American movie released in 1996.S2 In Japan, the film's title is written as "Maazu Atakku!" (マーズ・アタック！), which translates to "Mars Attack!".
* Yuggoth is the name of a fictional planet in the Cthulhu Mythos.
"Ideal and reality are still unreachable, but even so, there's no choice but to start running." (6:36)
The Japanese line is "Risou to genjitsu ha mada todokanai keredo, sore demo hashiridasu shika nai" (理想と現実はまだ届かないけれど、それでも走り出すしかない). This is referencing "Kamen Rider AGITO 24.7 version" (仮面ライダーAGITO 24.7 version), a song sung by Ishihara Shinichi (石原慎一) and released in 2001. "Kamen Rider AGITO 24.7 version" is the second opening theme song for "Kamen Rider Agito" (仮面ライダーアギト), a Japanese TV show about a masked super hero that aired from 2001 to 2002.S2 The original line goes, "Mada, todokanai risou to genjitsu sore demo, hashiridasu" (まだ、届かない理想と現実 それでも、走り出す), which translates to "Ideal and reality are still unreachable, but even so, I start running".
"Isn't it great? It's 'The Messenger from Yuggoth!'" (6:51)
The title of the song used as Nyaruko's ring tone is "Yugosu Yori no Shisha" (ユゴスよりの使者), which translates to "The Messenger from Yuggoth". This is referencing "Nichiyoubi Yori no Shisha" (日曜日よりの使者), "The Messenger from Sunday", a song sung by THE HIGH-LOWS and released in 2004.S2
"Buhho Konsherun!" (7:28)
"Buhho Konsherun" (ブッホ・コンツェルン), "Buch Concern", is the name of a group of companies in "Mobile Suit Gundam F91" (機動戦士ガンダムF91), an anime movie released in 1991.S1
"They're Mi-Go. They're called the fungi from Yuggoth. They're aliens that come from Pluto." (9:22)
There are four references here:
* Mi-Go is a species of creature in the Cthulhu Mythos.
* In "The Whisperer in Darkness", a short story written by H. P. Lovecraft and first published in 1931, it is stated, "They were pinkish things about five feet long; with crustaceous bodies bearing vast pairs of dorsal fins or membraneous wings and several sets of articulated limbs, and with a sort of convoluted ellipsoid, covered with multitudes of very short antennae, where a head would ordinarily be." In addition, it is stated, "They talked with their heads, which changed colour in different ways to mean different things."
* Mi-Go are known as "fungi from Yuggoth", as mentioned in "The Whisperer in Darkness". Hasta says the Mi-Go are called "Yugosu yori no mono" (ユゴスよりのもの), which translates to "things from Yuggoth".
* In "At the Mountains of Madness", a story written by H. P. Lovecraft and first published in 1936, it is stated that the Mi-Go came to Earth from Pluto. In addition, in "The Whisperer in Darkness", the narrator, Albert N. Wilmarth, suspects that Pluto and Yuggoth are the same planet.
"I'll use that money to go to the pure gentleman's meeting place, the Dreamland Club, and meet Amane!" (11:14)
There are four references here:
* "Doriimurando" (ドリームランド), "Dreamland", is referencing the Dreamland, a fictional location in the Cthulhu Mythos that humans can enter when they fall asleep.
* "Doriimurando Kurabu" (ドリームランドクラブ), "Dreamland Club", is referencing "Doriimu Kurabu" (ドリームクラブ), "Dream Club", a video game released in 2009.S2
* "Pyua na shinshi no shakouba" (ピュアな紳士の社交場), "pure gentleman's meeting place", is also referencing "Dream Club".S2 On the official website for "Dream Club", the following is stated.
"Touten ha, pyua na kokoro no mochinushi dake ga nyuuten dekiru kaiinsei no omise desu."
"Only those possessing pure hearts can become members of this establishment."
Image for reference:
Source of image: http://www.d3p.co.jp/dreamclub_first/
* Amane (アマネ) is referencing Amane (亜麻音), the main heroine of "Dream Club".S2
Hasta snaps his fingers to release blades of wind. This is referencing Fabulous Fitzkarald (素晴らしきヒィッツカラルド) from "Jaianto Robo THE ANIMATION -Chikyuu ga Seishi Suru Hi" (ジャイアントロボ THE ANIMATION -地球が静止する日), "GIANT ROBO THE ANIMATION -THE DAY THE EARTH STOOD STILL", an anime series released from 1992 to 1998. In the series, Fitzkarald has the ability to release energy that can slice through objects from his hands by snapping his fingers.
This crystal is based on the Shining Trapezohedron, a mystical crystal that is said to be a window on all time and space. It first appeared in "The Haunter of the Dark", a story written by H. P. Lovecraft and first published in 1936. The Shining Trapezohedron is capable of summoning Nyarlathotep.
"I have arrived!" (13:44)
The Japanese line is "Watashi sanjou!" (私参上！). This is referencing a catch phrase said by Momotarosu in "Kamen Rider Den-O" (仮面ライダー電王), a Japanese TV show about a masked super hero that aired from 2007 to 2008. His line goes, "Ore sanjou!" (俺参上！), which has the same meaning as above.
"There's a love heart in my chest, too! Accept it straight on, destiny!" (14:06)
The Japanese line is "Watashi no mune ni mo rabu haato! Massugu uketomete desutinii" (私の胸にもラブハート！まっすぐ受け止めてデスティニー！). This is referencing a line in the lyrics to "Totsugeki Rabu Haato" (突撃ラブハート), "Charging Love Heart". "Totsugeki Rabu Haato" is an insert song used in "Macross 7" (マクロス7), an anime series that aired from 1994 to 1995.S1 The original line goes, "Omae no mune ni mo rabu haato massugu uketomete desutinii" (お前の胸にもラブハート まっすぐ受け止めてデスティニー), which translates to "There's a love heart in your chest, too. Accept it straight on, destiny".
"Shell Bullet of!" (15:39)
The Japanese line is "Danzai no!" (断罪の！). Nyaruko was about to say "Danzai no Sheru Buritto" (断罪のシェルブリット), which translates to "Shell Bullet of Conviction". This is referencing Kazuma from "s.CRY.ed" (スクライド), an anime series that aired in 2001. A drama CD for the series titled "s.CRY.ed sound edition 1" (スクライド サウンドエディション1) was released in 2001. One of the tracks on this CD is titled "s.CRY.ed Comic Edition 'Treasoner'" (スクライド コミック・エディション「トリーズナー」). One of Kazuma's lines from this track goes as follows.S5
"Shinnen wo dangan ni kome, uchidasu! Kore ga, ore no hissatsu waza! Danzai no Sheru Buritto da!"
"I load conviction into a bullet, and shoot! This is, my certain kill technique! The Shell Bullet of Conviction!"
"Faundeeshon" (ファウンデーション), "foundation", is possibly referencing "Kougami Faundeeshon" (鴻上ファウンデーション), "Kougami Foundation", from "Kamen Rider OOO" (仮面ライダーオーズ), a Japanese TV show about a masked super hero that aired from 2010 to 2011.S2
"Function key!" (16:19)
"Fankushon kii" (ファンクションキー), "function key", is a button on some keyboards.S2
"Buiefu wan" (ブイエフワン), "VF-1", is referencing the VF-1 Valkyrie (VF-1 バルキリー) from "Chou Jikuu Yousai Makurosu" (超時空要塞マクロス), "Super Dimension Fortress Macross", an anime series that aired from 1982 to 1983.S2 The VF-1 Valkyrie is an aircraft that is shaped like a jet fighter plane and can transform into various forms.
"Big one!" (17:33)
"Biggu Wan" (ビッグワン), "Big One", is the name of a character from "Jakkaa Dengekitai" (ジャッカー電撃隊), "J.A.K.Q. Electrifying Squadron", a Japanese TV show about a squad of costumed super heroes that aired in 1977.S2
"Stop it! Stop the song!" (19:18)
The Japanese line is "Yamero! U, Uta wo yamero!" (やめろ！う、歌をやめろ！). This is referencing a line said by Giigu (ギーグ) in "MOTHER" (マザー), a video game released in 1989.S2 Its line goes, "U Uta wo yamero!" (う うたを やめろ！), which translates to "Stop the song!".
The heads of the Mi-Go explode due to hearing the song. This is referencing how the heads of the Martians explode due to hearing the song "Indian Love Call" sung by Slim Whitman in "Mars Attacks!".S1
"Plug in. The Messenger from Yuggoth. Transmission." (19:50)
The Japanese line is "Puragu in. Yugosu yori no shisha. Toransumisshon" (プラグイン。ユゴスよりの使者。トランスミッション). This is referencing a line said by Hikari Netto (光熱斗) in "Mega Man Battle Network" (バトルネットワーク ロックマンエグゼ), a video game released in 2001.S1 His line goes, "Puragu in! Rokkuman eguze, toransumisshon!" (プラグイン！！ロックマン.EXE、トランスミッション！), which translates to "Plug in! Rockman.EXE, transmission!". Image for reference:
"Why were we defeated, by this song?" (20:17)
The Japanese line is "Naze wareware ha, konna uta ni yabureta no da?" (なぜ我々は、こんな歌に破れたのだ？). This is referencing a line said by Giigu (ギーグ) in "MOTHER" (マザー).S2 Its line goes, "Naze kono watashi ga konna uta ni yabureta no da...." (ナゼ コノワタシガ コンナウタニ ヤブレタノダ・・・・), which translates to, "Why was I defeated by this song....".
"Even though I gallantly appeared" (20:41)
The Japanese line is "Sassou toujou shita no ni" (颯爽登場したのに). This is referencing a catch phrase said by Tsunashi Takuto (ツナシ・タクト) in "STAR DRIVER Kagayaki no Takuto" (STAR DRIVER 輝きのタクト), "STAR DRIVER: Takuto of the Radiance", an anime series that aired from 2010 to 2011.S2 His line goes, "Sassou Toujou! Ginga Bishounen, Taubaan!" (颯爽登場！銀河美少年、タウバーン！), which translates to "Gallantly appearing! Galactic Pretty Boy, Tauburn!".
(23:41 - 23:51)
The scene during this time is from the OVA episode of "Haiyore! Nyaruko-san". Post for reference: http://nyaruref.blogspot.com/2013/05/haiyore-nyaruko-san-ova-references.html
Iron Striver's pose is mimicking that of Kamen Rider 1 from "Kamen Rider" (仮面ライダー), a Japanese TV show about a masked super hero that aired from 1971 to 1973. Image for reference:
"My Mahiro and the Evil Gods fight too much!" (24:14)
The Japanese line is "Watashi no Mahiro-san to Jashin tachi ga shuraba sugiru!" (私の真尋さんと邪神たちが修羅場すぎる！). This is referencing "Ore no Kanojo to Osananajimi ga Shuraba Sugiru" (俺の彼女と幼なじみが修羅場すぎる), "My Girlfriend and My Childhood Friend Fight Too Much", a light novel series written by Yuuji Yuuji (裕時悠示) and published from 2011 and is currently ongoing.S1
"Bout High School!" (24:21)
Mahiro says, "Riaru" (リアル), and Nyaruko says, "Bauto Hai Sukuuru!" (バウトハイスクール！). This is referencing "Shoukan Kyoushi Riaru Bauto Hai Sukuuru" (召喚教師リアルバウトハイスクール), "Summoned Teacher Real Bout High School", a light novel series written by Saiga Reiji (雑賀礼史) and published from 1997 to 2010.S2
"Good self-performance!" (24:22)
The Japanese line is "Jienotsu!" (自演乙！). This is the name of a club which the main characters are a part of in "Ore no Kanojo to Osananajimi ga Shuraba Sugiru" (俺の彼女と幼なじみが修羅場すぎる), "My Girlfriend and My Childhood Friend Fight Too Much".S2 The name "Jienotsu" (自演乙) is actually a shortening for "Mizukara wo Enshutsu Suru Otome no Kai" (自らを演出する乙女の会), which translates to "Club for Maidens to Produce Themselves".
List of Sources:
S1. Comments on this post
S2. A post at Steman Blog (ステマブログ)
S3. A blog by servitors about Cthulhu Mythos inspired works (クトゥルー／クトゥルフ神話作品発掘記)
S5. Japanese Nyaruko References Wiki (這いよれ！ ニャル子さん 元ネタwiki) - Volume 7, Chapter 5
Thanks to everyone who contributed! This list wouldn't be nearly as long without you all. See you next episode!
Last updated June 21, 2013