I've noticed other reviews with reference to them, and since I have yet to see them, I'm just going to do a Raw Review. Anyway, you don't really have to have watched the others to understand this.
Initially, Haiyore! Nyaruko-san is about an alien (later to develop into a group of aliens) disguising herself(themselves) as humans to protect earth. Although this may make it seem to be an anime based on the supernatural and alien-like, it's not.
Hayore! Nyaruko-san is more focused on the daily life of our male protagonist while trying to adapt to his unwanted distractions. Hayore!'s plot-line is very Harem-like, as there are three characters that share a (weird) relationship with our main man. (They share a house too!) Although you can't really call it much of a Harem. (you'll see once you watch at least half of it..)
The plot though is very loosely tied. It does'nt really have much of a story-line. So it's not really a serious anime. There will be times when you may get tired of watching it too. The anime is focused more on Comedy, so expect a lot of that.
The art is more on the "moe" side, so expect a lot of "Kawaii!!!" moments. It also offers a colorful background and a very nice array of colors through the different worlds. Although most of the times, the story takes the seriousness out of the area and just adds more comedy.
All in all, Hayore! Hyaruko-san is definitely a must-watch to those who want a comedic, lighthearted anime which doesn't need much brain power to comprehend... Except maybe the Space CQC thing, which totally takes away the "close quarters" in "close quarter combat"
