From "The Word Detective" (about whose credibility I know nothing):

Since we're still on our extended coffee break, I'll take this opportunity to answer the question you folks didn't ask, namely what "catawampus" (as I'll spell it) actually means. Once again, however, the answer is not simple because the word actually has two quite distinct meanings. A "catawampus" can be a fierce, imaginary animal, the sort of vicious critter that jumps you in the woods shortly before you're never seen again. But "catawampus" can also mean "askew" or "out of whack," as in "Larry's elopement with Eloise knocked Cindy's wedding plans all catawampus." Neither meaning can be definitively traced, but "catawampus" in the eat-you-alive sense may well be a variant on the American folk term "catamount," short for "catamountain," or mountain lion.

The "askew" sense of "catawampus" is a real puzzler. The first element of the word, "cata," may be related to "cater," also found in the related word "catercorner" (or, as many folks know it, "cattycorner" or "kittycorner"). "Cater" in these words comes from the French "quatre," or "four," and "catercornered" originally just meant "four-cornered." Today "catercorner" means that two things are diagonally across from each other. The "wampus" part may have come from the Scots word "wampish," meaning "to wriggle or twist," which would certainly seem to fit with "catawampus" meaning "askew" or "crooked."