When I first heard this word used - just last month - I thought it was spelled "kattywompous" perhaps in adjectival rhyme with "pompous." Alternate spellings are many but catawampus appears to be a close second. As words of the days go, cattywampus was pretty elusive.
Cattywampus is not the activity that your cat engages in between 3:30 and 4:15 every morning, nor is it the name of the sound the cat makes while doing it.
Persistent poking around got Urban Dictionary and Dicitonary.com to agree that cattywampus means askew, awry, not centered or out of balance. I'm definitely going to start using this word whenever things are out of alignment or in need of knolling. There's also a secondary meaning of something like "not directly across from" in contrast to catty-corner aka catercorner. Seems like a not very useful way to give directions, "it's cattywampus from the Dunkin Donuts, you can't miss it."
As appealing as the idea seems, cattywampus is also probably not related, at least not linguistically, to koyaanisqatsi, which means "life out of balance" in Hopi.
Bonus round: in a literally Sophomoric move, a Wisconsin college basketball player last March used the word cattywampus in an effort to foil the stenographer transcribing his interview.