Something that's off-kilter, crooked, or strangely twisted is cockeyed. If the cockeyed pictures on your grandparents' wall drive you crazy, you may need to go around their house straightening them all.
If your hat's on cockeyed, it's askew, leaning to one side, and if the lights on your friend's Christmas tree are cockeyed, they're drooping in a lopsided way. Something that doesn't make sense or isn't believable can also be called cockeyed: "Then he told this cockeyed story about having lunch with the President." In the 1920s and 30s, the word also meant "drunk." It started out, in the 19th century, meaning "squint-eyed."