Mahiro (Eri Kitamura) is warned by Nyarko during Episode 8's WORKING!! parody that unless he is careful in dealing with his coworkers, a beautiful girl with a katana may cut him off, alluding to Kitamura's role in said show as Yachiyo Todoroki, and in Episode 9 he (in Nyarko's body and voiced by Asumi) quips the famous "I'm so stupid" quote of Sayaka Mikimoments before she is turned into a Witch.
Considering the titular character, Nyarlathotep references are common
In the Mythos, Nyarlathotep can change to a wide range of forms, including some horrific humans. While unlikely, it won't be too farfetched to assume that this Eldritch Abomination can take the form of a bubbly schoolgirl.
Mahiro: "I don't need a thousand-faced little sister!"
The three-lobed red single eye in darkness with bat wings is a form of Nyarlathotep described in The Haunter in the Dark... and a description of Nyarko's Henshin Hero form's helmet.
Nyarko's brother, Nyar-o, has a pharaoh-like costume. Another usual trait of Nyarlathotep is being associated with Ancient Egypt (thus the "-hotep" suffix).
Nyar-o's Full Force Form resembles yet another known avatar of Nyarlathotep - The Bloody Tongue - which is encountered in the Call Of Cthulhu adventure module Masks of Nyarlathotep.
One of Nyar-o's grunts is "Tezcatlipoca!", alluding to the Aztec god of destiny being one of Nyarlathotep's avatars in the Call Of Cthulhu RPG.
Nyarko's police car is called... the Nephren-Car. Nephren-ka, otherwise known as the "Black Pharaoh", is, depending on the source (Robert Bloch's Mythos stories or Call Of Cthulhu), a corrupt pharaoh who is either a devotee of Nyarlathotep or the deity himself under one of his many guises.
Cuuko's crush on Nyarko is likely a reference to August Derleth's "The Dweller in Darkness", where their namesake gods appear in the story, one being used to fight off the other.
Nyarko's pet Shantak-kun is weak against Nightgaunts. In "The Dream Quest Of Unknown Kadath", Shantaks fear Nightgaunts, servants of Nodens, who himself plays a minor role in this series.
The superhero show in Episode 1 mentions "Star Vampire Crusaders" in Gratuitous English. Star Vampires are another mythos species.
R'lyeh, the eldritch house of Cthulhu... turns out to be an amusement park. The "taxi" taking Mahiro and Nyarko to R'lyeh is Dagon, the male leader of the Deep Ones, worshipers of Cthulhu in the original Mythos.
The "BLT" sandwich from Episode 1 of the anime means "Byakhee, Lloigor and Tsathoggua". Unlike the first two, the latter is not a species, but an individual Great Old One. This may or may not be an error — she might be referring erroneously to the whole species by that name, as most mythos gods are members of wider species in this series, but generally with an added suffix, not given in this case, to differentiate each member. But being Nyarlathotep, wanting a specific Great Old One for a sandwich ingredient isn't out of the question either.
From Episode 5 Nyarko quips "You fool, Cuuko is dead!", taken from The Statement of Randolph Carter (replacing "Warren").
The video game rivalry between Cthulhu Corp. (of which Luhy was an employee) and the Carcossa Computer Entertainment (owned by Hasta's father) alludes to Hastur and Cthulhu'sSibling Rivalry.
Hasta was once employed as a "librarian at Celaeno Library". In The Trail Of Cthulhu, the Library is a repository of elder lore on another planet. Byakhee, servants of Hastur, infest the place and can take travelers there.