Nihilego is obviously based off of a jellyfish. Jellyfish inject a neurotoxin into their prey when they sting, paralyzing them — this is probably the inspiration for Nihilego's ability to affect people's minds. Bulbapedia explains what species of jellyfish this Ultra Beast might be based on. As well as jellyfish, Nihilego draws inspiration from parasitic organisms.
Buzzwole is a mosquito. Its proboscis is the most obvious clue, but Buzzwole's "muscles" also bear similarities to a mosquito's bloated abdomen when it is full of blood.
Pheromosa is based on cockroaches. Specifically, cockroaches that have recently moulted. When a cockroach shed its old exoskeleton, the new one is a pale white colour until it hardens. It looks a lot like Pheromosa. Bulbapedia tells me it also looks a lot like a copepod, tiny freshwater organisms with long antennae. When searching for a mate, he females emit pheromones for the males to follow.
Xurkitree is a basically bunch of wires tied together with plastic zip-ties. Its "hands" look like the copper strands you can see when you cut a wire. It also looks like a tree, and can learn Ingrain. Also it's the best Ultra Beast because it looks like this bad boy.
Celesteela loosely resembles a rocket, particularly the arms. Its arms and parts of its body look like bamboo shoots. The strongest inspiration for Celsteela, though, is The Tale of the Bamboo Cutter, a Japanese folk story about a man who finds a baby inside a stalk of bamboo. When she grows up she learns that she is not from Earth, but rather the Moon, and she must return. This story probably inspired Celesteela's rocket design. Celesteela looks like it is wearing a multilayered kimono, or a jūnihitoe.
Kartana looks like an origami paper doll. Its head somewhat resembles the helmet of a samurai. Its whole cutting theme is a joke about papercuts. Its sharpness and sword-like arms, as well as its folded appearance, could be a inspired by the way Japanese swords were made — by repeatedly heating, folding and layering thin pieces of metal into a deadly blade. Speaking of swords, Kartana's name is obviously a pun on the Japanese katanas and, maybe, the British curtana.
Guzzlord is a tough one. I swear I've read about some mythological creature that devours mountains, but I cannot find it on the internet. Bulbapedia suggests that its ability to eat anything, and the fact that what goes into Guzzlord never comes out, could point to it being based off of a black hole. It also looks kind of like a crab, I guess. The clawed "tongues" that come out of the corner of its mouth look kind of like a xenomorph's inner jaw, although the rest of its fat body looks nothing like the lithe alien.
Necrozma is a prism — it refracts light. This explains where it fits in with Solgaleo and Lunala. The sun and the moon emit light (well technically the moon just reflects sunlight but blah blah blah), a prisms absorb and refract light. We'll probably get a better explanation of Necrozma's origins in Ultra Sun and Ultra Moon.