The "askew" sense of "catawampus" is a real puzzler. The first element of the word, "cata,"
may be related to "cater," ... from the French "quatre," or "four," and "catercornered" originally just meant "four-cornered."

I wonder if the Greek "cata-" could have crept in somewhere too. That would be cata- (opposite is "ana-") meaning destruction/tearing down, as in catastrophe and catabolism. Or is this just convergent evolution?