oddball vs nut case

oddball and nut case both are nouns.

Word	Noun	Adjective	Verb	Adverb
oddball	Yes	No	No	No
nut case	Yes	No	No	No

As nouns, nut case is a hyponym of oddball; that is, nut case is a word with a more specific, narrower meaning than oddball:

Other hyponyms of oddball include crackpot, crank, fruitcake, nut, screwball, nutter, wacko, whacko.

oddball (noun)	nut case (noun)
a person with an unusual or odd personality	a whimsically eccentric person