rarity vs oddment

rarity and oddment both are nouns.

Word	Noun	Adjective	Verb	Adverb
rarity	Yes	No	No	No
oddment	Yes	No	No	No

As nouns, rarity and oddment are synonyms defined as:

Other synonyms of rarity include curio, curiosity, oddity, peculiarity.

rarity (noun)	oddment (noun)
something unusual -- perhaps worthy of collecting	a piece of cloth that is left over after the rest has been used or sold
a rarified quality	something unusual -- perhaps worthy of collecting
noteworthy scarcity