American slang. Defined, when included, by slang dictionaries as the state of being grossly out of alignment, skewed or as out of alignment.
One dictionary I found says it is synonomous with kittycorner, though that seems incorrect. I've always used the two words as distinct, kattywampus meaning "out of kilter" and kittycorner meaning "off set" Closely related, but distinct by the later being a wrong state of affairs, or by being katterwacked, all messed up and out of wack, a word I found while poking slang dictionaries.
Alternate spellings are (k)(c)a-(tt)(dd)-(i)(y)-w-(a)(o)mpus, in pretty much every combination, though I prefer kattywampus.
Two bands use the name Kattywompus, a string band and a metal band while a funk rock band uses the name Cattywompus.