The MOST random character in DC? I think every batman villain ever might have a run at that title. A crazy clown murderer, a murderer who communicates in riddles, a penguinish fellow who kills people with weapons themed on his friendly arctic look-alikes, a giant crocodile man, someones who's face got partially burned so BAM...murder.
Catwoman is just a bad pun on cat burglars, so that's better. I think.
Almost all comic book characters are hella random without suspension of disbelief. Is half demon as ridiculous as a fish speaking KING of Atlantis?