Not the weirdest maybe, but the ugliest... their own piece of...poop!
Casper did that once, and we didn't find it funny at all. Apparantely he had done the job in the morning, and then the poop was hard enough to be played with later that day, so he just punched it outside the litterbox, and was punching it then on the floor...YUCK!!! Needless to say that we found it very disgusting. Luckily since then, they play with other stuff.