I'm fond of the original show, Nyaruko: Crawling with Love, despite being rude about it in a review and often finding it annoying harem nonsense. The sanity-shattering abominations of H.P. Lovecraft's novels are real and visiting Earth in attractive human forms. Three of them (Nyarlathotep, Cthugha and Hastur) move in with a downright hostile human schoolboy (Mahiro Yasaka) and all want to have sex with him.
THE FULL SERIES
2009: Haiyoru Nyaruani OVA (9 web micro-episodes) = you can skip these, although they're the only place where Mahiro's fork-stabbing is funny.
2010: Haiyoru Nyaruani Remember My Mr Lovecraft (12 web micro-episodes) = slightly chunkier, with a plot.
2011: Haiyore! Nyaruko-san (12 TV episodes followed by an OVA) = start here. The web micro-episodes aren't part of TV continuity. If nothing else, it has a fun title sequence. Bouncy, evil song from the depths of blasphemous abomination, plus sexy legs.
2012: Haiyore! Nyaruko-san W (12 TV episodes followed by another OVA) = the sequel. I like this title sequence too.
2015: Haiyore! Nyaruko-san F (one-off OVA episode) = planned as the first of an OVA series that would have completed the adaptation of the novels. That never happened, perhaps partly due to the death of Miyu Matsuki (who played Kuuko) at the age of 38.
Now for the three OVAs, which I only discovered recently:
[OVA #1] "JUST LIKE A SEQUEL" (2011, 15 minutes)
The funniest of these three OVAs and the only one without "series ending" responsibilities concerning the Nyaruko-Mahiro relationship. Nyarlathotep becomes a magical girl. (Cthulhu takes her into Hyperbolic Time, where a day in the outside world will allow a year of training.)
For about two minutes, this seems to have worked. "There's nothing scary about me any more!" However, on finding some "naughty kiddies" (i.e. nightgaunts), Magical Girl Crawling Nyarlathotep pulls a crowbar from her crotch, uses it as a magical wand and blasts them with death magic. She then goes a bit nuts. "The only good kiddie is a dead one! I've already started, so why don't I carry your corpses to heaven as well?"
She burns them, then stamps on the bodies. She decides to cleanse the planet Earth of all "naughty kiddies".
Fortunately, Cthugha appears to have mugged the Men in Black.
[OVA #2] "A KIND WAY TO KILL ENEMIES" (2012, 15 minutes)
A hot springs episode, with rampant but discreet nudity. Absolutely no nipples. Naturally, the extraterrestrial sex maniacs are nothing but trouble. Nyarlathotep puts an aphrodisiac in the water, but the "wrong" people are in there. (Did it even make that much difference to those two?) She also has a drug that turns you into an army of tiny dwarf copies of yourself, for a comedy chase sequence.
There's a comparatively deep Mahiro-Nyaruko conversation towards the end, but of course Nyaruko destroys it by being herself.
I don't like the sound effects they've added to the title sequence. I like the music. I want to listen to it!
[OVA #3] "HAIYORE! NYARUKO-SAN F" (2015, 28 minutes)
It has some good jokes. The episode opens with a dream sequence. "Yasaka Mahiro, do you take Nyarlathotep to be your lawful wedded wife?" The juxtaposition made me laugh. There's also a gag reference to a school idol anime.
Half of the episode is jolly nonsense. The token harem scenes of Nyarlathotep, Cthugha and Hastur competing to claim Mahiro's virginity can sod off, although fortunately they're brief. The gang get some tickets to go to an amusement park and play an escape game.
In the second half, though, Nyaruko's nervous system gets attacked by nanomachines that steal your memories and powers. Mahiro ends up carrying her. The conversation between them gives the episode more emotional depth and serves as a good finale for the series and its dysfunctional Nyaruko-Mahiro romance. The episode doesn't end with sex or marriage (although the light novels do and of course play it for horror-comedy), but they definitively kiss.
You can see the aborted plot continuations in that sinister woman who's walking on water, though. She has plans for the future.
Revisiting this series was quite nice. I like the cast. The harem silliness doesn't break the show, partly because there's not actually that much of it and partly because incomprehensible eldritch abominations can get away with anything. It's funny. If they ever returned to making F, I'd be surprised but I'd definitely watch it.