In Episode 1 of Nyaruani, Nyarko channels Setsuna F. Seiei as she declares "I am...we are...Cthulhu!"
Episode 9 of the first Nyaruani has Nyarko say that in space kindergarten, she went around looking for kids playing make-believe and beat them up, with the Catch Phrase "I'll shatter that pretend game of yours!" This earned her the nickname "Slacker Breaker"note In Japanese, Himagin Breaker. In case you missed the reference, they just go ahead and throw up a title card that reads "A Certain Slacker-Breaking Nyarko", with a silhouette of Touma behind it.
Cuuko's story about why she fell for Nyarko involves her being forced to play the bad guy in a pretend Saint Seiya game; one of the other games Nyarko mentions busting up is "Federation vs. Principality", with censored-out Bright Noah and Garma Zabi (and Nyarko in Sayla Mass's uniform).
Episode 11 of Remember My Love(craft-sensei) has Nyarko assure Mahiro that everything would be alright as they would erase everyone's memories once they were done. Then she takes out the neuralyzer. Mahiro responds that something about that object seems familiar and gets a mental image of Tommy Lee Jones as Agent K.
On top of that, Mahiro's mental image of K is saying "There's coffee", referring to Jones appearing in a series of ads for UCC Coffee in Japan (in which, ironically, he plays an alien who's trying to understand human culture).
In episode 12 of Remember My Love(craft-sensei), Nyarko's description of Space Comiket includes an image of the Gaijin 4koma Reaction Guys.
In one episode, Cuuko quotes the line "swans look calm but are actually kicking furiously under the water" while a Fender bass guitar floats on the background, a reference to K-On's first season ED song lyrics.
The series loves to reference other (yes, there are more) "Moe Mythos" series. In Episode 1, a little figurine on the anime store is the version of Nyarlathotep from the manga Igyou tachi ni yoru to sekai ha.... The cover of the "recalled eroge" is from Maumi Shoujo R'lyeh ruru light novels. And two girls in Mahiro's class are characters from R'lyeh High School, which shares the same illustrator with this series, Koin. The mech Demonbane make brief cameo in episode 11.
"SAN" is an attribute in the classic Tabletop RPG Call of Cthulhu by Chaosium. You can even see a glimpse of a character sheet and the trademark percentile dice of the Chaosium RPG systems in the first episode, and a Storyteller screen in the ED. The roll shown is accurate as well, illustrating either a legitimate failed SAN roll (with the amount of lost sanity not shown), or the roll for said amount. Incidentally, a d100 like the one shown would be appropriate for seeing Nyarlathotep in one of its monstrous forms.
In addition, the title cards in Nyarko-San W show Nyarko standing on top of a Cthulhu Dice d12 made by Steve Jackson Games.
You could make a subpage just to cover this series' references to Kamen Rider, since there's at least one per episode. In fact, Kamen Rider is the very first pop culture reference they make in the 2012 series, with Nyarko performing Takeshi Hongo (Rider #1)'s transformation pose when she introduces herself to Mahiro (and she makes Hayato Ichimonji (Rider #2)'s pose when she surprises him in the bathtub at the end of that episode). A few more:
Per Word of God, Nyarko's "Full Force Form" is a direct homage to Knight Blazer from Wild ARMs 2; however, other aspects are nods to Kamen Rider, with the name probably being a reference to Kamen Rider Kabuto, which had an insert song named "Full Force".
The individual series with the most Shout outs is Kamen Rider Double; in fact, Nyarko-san W is specifically named after it. Ironically, that series contains more references to Kamen Rider Wizard, because Nyarko-san W aired alongside episodes 30-40 of Wizard.
Fifth episode has another single yelp, this time from Kinniku Man (Hell Missionaries)
Nyarko-san W has an episode where Nyarko's yelps are the names of Kamen Rider OOO's alternate forms; the villain of the later episode "High School of the Heat" continues this reference by shouting "Sagohzou!" when defeated.
Nyarko recreates the famous "Beergasm" from Neon Genesis Evangelion, only with a bowl of miso soup in place of beer.
The subtitle of the then-current season of Iron Striver is Star Vampire Crusaders, combining Star Vampires (a type of monster from the Cthulhu Mythos) with Stardust Crusaders (the third and best-known story arc of JoJo's Bizarre Adventure).
The sequence where Mahiro and Nyarko sail to R'lyeh is a long set of Shout Outs to One Piece, with Nyarko repeatedly referencing the manga's plot (and getting shut down by Mahiro) as well as the sail bearing a version of the Straw Hats' skull-and-crossbones emblem with Nyarko's trademark Ahoge.
This one is made even more blatant in the light novels, where Nyarko defends the use of the grenade by saying "King Arthur used one in the battle of Antioch" and Mahiro replies "That was Monty Python!"
The description Nodens gives for the Boys Love show he wanted Mahiro to star in ("It's a sparkly love-hate drama about a pretty boy bought by a young businessman.") sounds a lot like Okane Ga Nai.
Nodens sends Nyarko and Cuuko to battle in Another Dimension; this is a nod to the Space Sheriff sub-series of Metal Heroes (including Gavan, Sharivan, and Shaider), where each series' villains had their own dimension that made their monsters stronger and the hero weaker.
R'lyehland's mascot, Insmouthboy, looks a lot like another fish-boy, Ponyo
The light novels dip into Does This Remind You of Anything? territory when Nyarko says that the Cthulhu Corporation fought tooth and nail to maintain their trademark on Insmouthboy until they eventually got passed a law specifically to keep him out of the public domain, making him an obvious play on Mickey Mouse.
Episode 3: "Mahiro Yasaka Wants to Live in Peace", referring to "Yoshikage Kira Wants to Live in Peace" (the 37th volume of JoJo's Bizarre Adventure)
Nyarko asks Mahiro if he wants her to call him "Nii-nii". That term is frequently used by Miya Tachibana, who, like Nyarko, is voiced by Kana Asumi.
Nyarko goes on to make a gununu face when confronted with the DK-do cake. Also from Ichigo Mashimaro, Cuuko's face-plant is a trademark of that series resident twintails, Miu.
"Trapezohedrons are Unbreakable", the subtitle for the newest Iron Striver series, is a combined reference to JoJo's Bizarre Adventure ("Diamonds are unbreakable") and the Cthulhu Mythos (the Shining Trapezohedron from Lovecraft's The Haunter in the Dark).
Yoriko's introduction as a Deity Hunter makes multiple references to Monster Hunter. The music in the background, Yokiro's hunting outfit and the artwork of the monster in a cover of a book (called "Deity Hunter Frontier") takes clear inspiration from the series.
When Mahiro learns that Hasta had to perform CPR on him and thus has stolen his first kiss, he mutters "No count, no count!" in Gratuitous English, just like Kaoru did in Amagami SS when she accidentally kissed Junichi. That would make it the second Kaoru reference in the series, if you count Nyarko using her belly-exposing stance in episode three.
Nyarko follows the Ran Mori school of thinking: karate kicks can solve anything!
The Nephren-car can negotiate even Red Canyon and Fire Field! Good thing if you're playing F-Zero.
Episode 5: "Great Conspiracy X", referring to "Great C", a 1990 short story by Brian Lumley.
five Hasta says he wants to "combine" with Mahiro. At the end of the preview for the next episode, Mahiro asks why Nyarko hasn't made a "combine" robot joke this time: Nyarko answers that "it was a little too adult". Of course, there's a Humongous Mecha series where mecha "combining" has a Does This Remind You of Anything? quality, Sousei No Aquarion. Hasta also has an unusually sharp sense of smell, just like Aquarion's Apollo, and he makes an absurdly long-reach love promise with Mahiro, too.
Mahiro and Cuuko's first encounter is from Maria-sama Ga Miteru (except here, it's Azathoth watching over them).
There are numerous references to Haruhi Suzumiya: Cuuko mentions "Endless Eight"; later she impersonates Ryoko Asakura, sans the cheerful disposition and with a BFS instead of the knife. Immediately after we see Nyarko in a Playboy Bunny getup attempting to play the Lovecraftian version of "God Knows".
They actually had to tone one of these references down; the Next Episode preview for #9 shows Cuuko's uniform is blue, exactly like those in Haruhi, but in the episode itself the uniform is green.
In the fight scene, Nyarko is dressed as Pai Chan, Cuuko as Mai Shiranui, and Hasta as Bridget. The stats given are their actual ones from the Call of Cthulhu RPGnote Except for Hasta's, which uses Cuuko's stats apparently due to a mix-up with the staff.
Before starting the fight, Nyarko quotes the taglines for Kamen Rider 555, Agito, and Ryuki in succession ("Racing instinct! Awaken that soul! Those who don't fight don't survive!")
The Gay Option ending from True Love 95 gets brought up as a possible route by Yoriko, who tells her son that even Yoichi, his Bromantic Foil, might confess to having feelings for him, just like how Kazuhiko Miyoshi, the foil in that game, did the same towards the end of the game if the player was unable to choose a girl for Daisuke.
Mahiro, while inside Nyarko's body, commands Kuuko to take Nyarko (who's inside Mahiro's body) and Hasta to the living room so that they wouldn't bother him. He promises her a contract in which Nyarko will give her body and soul to her in exchange. His movement when "commanding" her is similar to Lelouch from Code Geass, while Kuuko responds with "Yes, your Highness."
The image of M-Nyarko commanding looks an awful lot like the famous "OBJECTION!" pose.
Episode 11: "Lost Girl from the Stars", a play on "Shambler from the Stars" by Robert Bloch
The episode starts with the alien trio waking Mahiro by playing Mario Kart (apparently 64) in his bedroom.
The later part of the episode recalls the second Urusei Yatsura movie, which sees the main cast trapped in a "Groundhog Day" Loop in an empty city, just like Mahiro. There are several shots that are direct Homages to said movie as well.
Episode 12: "He Waits, Dreaming", a Cthulhu Mythos reference (specifically to the original story "The Call of Cthulhu")
When Nyarko shows Mahiro the Mirror of Nitocris, she actually quotes Kuso Miso Technique, the manga that originated the "Yaranaika?" meme.
During the final battle, Nyarko, Cuuko, Hasta, Luhy and Yoriko strike the Go-onger group pose.
Nyarko turns her crowbar into a giant sword and proclaims "Malign God Roar", just like in Demonbane.
Major Fogger paraphrases the Major's "I love war" speech, only with the war references change to Hentai games. He even name-drops Key Visual Arts and Leaf by using the Japanese words for them ("kagi" and "konoha").
This is accompanied by images of Nyarko dressed as Noumi Kudoryafuka and Amanatsu Purinnote from Hoshi no Ouji-kun Le prince de l'Etoile.
When Mahiro tells Nyarko to kick the villain's ass, she responds with the Dorombo Gang's trademark salute and "Ara, hora, sassa!"
OVA: "How to Defeat a Kind Enemy", a play on the light novel series "How to Kill a Kind Dragon"
The sequence we get to see of Iron Striver (Nyarko's favorite Toku show) leans heavily on Kamen Rider Decade, with the protagonist resembling actor Masahiro Inoue (but dressed kind of like Philip), saying "Bring it on! I'll destroy everything!" and transforming in exactly the same fashion as Tsukasa/Decade.
The opening sequence is a direct parody of Bewitched; the Opening Narration and title My Wife is Nyarlathotep are references to the Japanese dubbed version (which was retitled My Wife is a Witch).
The trio changes from pajamas to school uniforms using Kamen Rider Wizard's magic circle transformation, followed by Nyarko imitating his Connect Ring to summon her school bag. When Mahiro asks what that was, Nyarko says she wanted to try the "latest version's" transformation before cheering "Isn't it super-great? Isn't it the best?!", referencing the lines said by Wizard's belt when he activates a Finishing Move.
Immediately afterwards, she says she'll store their belongings in Mirror World until they have time to set up individual bedrooms.
While discussing Yamanso.Com, they work in two references to Lucky Star: Cuuko doing Konata's finger point, and Nyarko doing the famous "Darling Darling Please!" pose.
On top of that, the way Nyarko tries to reference AKB48 is by showing Mahiro a set of Gaia Memories from Kamen Rider Double; Double pulled this exact same referece in The Movie, as a nod to the fact that two of its minor characters, Queen and Elizabeth, were played by members of AKB48.
Tamao declares to Nyarko "A person's heart being stolen by another person's overwhelming power is without a doubt, love!", playing off of Graham Akre's declaration of "love" to Setsuna F. Seiei and his Gundam Exia.
The library's forbidden bookshelves are the Gaia Library; additionally, the search engine Mahiro and Hasta use to try and determine the girls' ages requires the use of three keywords, just like Philip's lookups.
Mahiro: "This is the first time in my life I've been provoked to hit a woman."
The Next Episode preview starts with Nyarko saying "These three things will happen next time! One!" When she doesn't follow this up, Mahiro asks what happened to them and she responds "The other two are just for decoration. The higher-ups...", referring to the dialog in Mobile Suit Gundam when Char receives the Zeong, asks about its lack of legs, and receives a similar response from the technician.
When Nyarko talks to Tamao about her attempts to charm Mahiro, she refers to her plans as Operation Yashima, Operation V, and the Black Rebellion; each scene is accompanied by a mental image of Nyarko imitating the anime she's referencing (using a giant sniper rifle, rising from a flatbed, and cackling evilly while dressed as Lelouch/Zero).
The infamous Daifugo sequence has Nyarko and Cuko playing cards using Kamen Rider Blades Rouze Cards, with Nyarko remarking that her existence is like an "eternal trump card" (the title of Blades final episode); and of course, the repeated shouts of "Cyclone!" "Joker!" refer to Kamen Rider Double's primary form, CycloneJoker.
When Mahiro is woken up by Nyarko, Wilson can be seen in the foreground.
In their last fight, Kuuko and Nyarko paraphrase the lyrics for Mazinger Z and Ore wa Great Mazinger.
Earlier during said fight, there are two moments where Nyarko and Cuuko paraphrase lines from Mobile Suit Gundam Wing, once from the TV series' final battle ("I refuse to acknowledge myself as a supporting character.") and once from Endless Waltz ("How many more times do I have to gut-punch you and your damn mobile turrets?!")
Cuuko's descriptions of Cuune's abilities are a mix of the theme song to Devilman and nods to Wild Arms and Ultraman. When she says "The coldness of her Aphoom-Zhah is negative one trillion degrees!", Mahiro responds "You can't just ignore the laws of physics like that!"; American fans might recognize that line better as "So much for the laws of physics!"
At one point Nyarko asks if the Banshin's brain is short-circuiting, quoting a line from "Moonlight Densetsu", Sailor Moon's opening theme.
OAD: "Goodbye to the W/A Chaotic Love for this Hot Spring", a reference to "Goodbye to the E/A Bouquet of Justice to This City" (the final episode of Kamen Rider Double).
Nyarko's recap of the finale episode uses a parody of the Attack on Titan opening.
Luhy and Yoriko strike the poses of every lead Precure except Megumi's when commenting on how effective the Forever 17 hot springs are.
Which may double as an Actor Allusion, since Kikuko Inoue played Yoriko in the drama CDs.
The covers of every light novel (sans the first) shows Nyarko doing a different Rider's transformation pose; these poses are used again in the opening sequence of Nyarko-san W. This gets taken a step further with Volume 8, which had two covers, the standard release where Nyarko imitates Kamen Rider Black and the limited edition where she imitates Kamen Rider Black RX. Combine the two, and you get a nod to Kamen Rider Decade which had Black and RX transform side-by-side for the first time.