The two words kirai (嫌い) and nikui (憎い) seem to be placed similarly in sentences and the definitions I've seen range from similar to almost identical, depending on the source. It's a bit confusing, but there must be some nuance to the distinction. My best guess is that it's intensity: nikui is stronger than kirai, in the same way that in English 'hate' is a stronger than 'dislike.' Is this correct? If not, what is the difference?
In checking my understanding of the grammar of the words, I also noticed that kirai is an adjectival noun (for a na-adjective) while nikui is an i-adjective.