(Adj.) Used to describe a dubious or made up word, term, or phrase that does not makes logical sense within existing language conventions but may make sense in a cultural context.
Examples of incromulent words are
Meh: (interjection) Mediocre; lackluster; unexceptional; uninspiring.
Asshat: Obnoxious person.
A person, of either gender, whose behavior displays such ignorance/obnoxiousness that you would like to make them wear their own ass as a hat.
Origin: The antonym of the word cromulent
Asshat is such a stupid word that is entirely incromulent.