disgrace vs odium

disgrace and odium both are nouns.

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

As nouns, odium is a hyponym of disgrace; that is, odium is a word with a more specific, narrower meaning than disgrace:

Other hyponyms of disgrace include humiliation, obloquy, opprobrium, reproach, cringe.

disgrace (noun)	odium (noun)
a state of dishonor	hate coupled with disgust
	state of disgrace resulting from detestable behavior

disgrace (verb)	odium (verb)
damage the reputation of
reduce in worth or character, usually verbally
bring shame or dishonor upon