Using neem oil for cats has the same benefits as using neem oil on dogs.
You can read more about neem uses and benefits, how to treat skin problems and parasites, and how to make sprays and shampoos, on those general dog and pet pages.
There is, however, one aspect of using neem oil on cats that is unique to cats, and that I wanted to address separately.
Cats are constantly licking, cleaning and grooming themselves, so whatever you put on them they will ingest. That makes the use of any chemicals or pesticides a particularly nasty option. What's a cat owner to do when a cat suffers from skin problems or parasites?
Neem pet shampoo is safe for cats, even for super sensitive, allergic-to-pretty-much-everything cats. In fact, you will probably find that the use of neem lowers your cat's sensitivity to environmental stresses significantly, and that its immune system in general improves.
However, not every neem shampoo or neem spray that's good for dogs is safe to use on cats!
But it's not the neem oil that is the culprit. The biggest problem with neem pet products is that many commercial neem pet shampoos or neem sprays also contain other essential oils, in particular tea tree oil.
Tea tree oil is not safe for cats!!
Essential oils are often used to mask the smell of neem oil, and cats are very sensitive to essential oils.
If you want to use neem products on your cat, make sure you buy something without tea tree oil in it, or cajeput, or camphor oils. Or even better, buy 100% pure organic neem tree oil, and mix it into the shampoo or product you usually use.
Ingestion is not a problem since the shampoo is rinsed out. You don't need to worry about neem oil traces. They do no harm. The smell left behind is enough to discourage fleas. If used at low concentrations, neem sprays are fine, too.
If it is safe for you to spray or bathe your water hating cat is of course a different question...
It's simple: use neem leaf on your cat.
Neem leaf is the preferred part of the neem tree in Ayurvedic medicine for treating any skin disorders. Neem leaf is totally safe, even if ingested in large quantities. In 5000 years nobody has ever reported any adverse affects or an overdose, not in humans or any animals, from using or taking neem leaf.
Neem oil on the other hand has shown some toxicity if ingested in large quantities. It is not sure if the toxicity was due to the neem oil itself or due to some contaminant in the oil. Still, I would not treat a cat with a concentrated neem oil product that's left on the coat/skin, especially when there is a perfectly safe alternative.