The weirdest, most hilarious thing is still what one of the jays did a few weeks back. We were putting out peanuts for around 4 of them. One of them grabbed a big peanut, the kind with two nuts in it.
They shelled the peanut, ate one of the nuts and...
...brought the other one back. Laid it neatly on the railing and returned to the tree.
I'm still not sure if that was sharing, "hey stupid did you know these have food in them?" or what. But it was VERY deliberate.