The first key can be found by popping the balloon and retrieving the key on the balcony in the castle.
The second key requires you to go back to the cave where the creature first chased you when you played the Jack-in-the-Box. Ride the red car around to the second world and grab the key at the end of the line.
The last key can only be retrieved by finding all twenty disks around the two worlds and placing them in any one of the viewers. After you put them all in, Willie will give you the last key.