odium vs hate

odium and hate both are nouns.

Word	Noun	Adjective	Verb	Adverb
odium	Yes	No	No	No
hate	Yes	No	Yes	No

As nouns, hate is a hypernym of odium; that is, hate is a word with a broader meaning than odium:

odium: hate coupled with disgust
hate: the emotion of intense dislike; a feeling of dislike so strong that it demands action

Other hypernyms of odium include disgust, hatred.

odium (noun)	hate (noun)
hate coupled with disgust	the emotion of intense dislike; a feeling of dislike so strong that it demands action
state of disgrace resulting from detestable behavior

odium (verb)	hate (verb)
	to have and express negative sentiments about a person
	dislike intensely; feel antipathy or aversion towards