In the PlayStation versions, one of the costumes is Sackboy from Little Big Planet
It looks like one half of Ben Burbank's Amnesia Fortnight pitch, Jet Girl & Ghost Dog, made it into the game.
The wolfman does the Thriller. Plus, his upgrade is Teen Wolfman. His name and appearance in this form is a reference to the film Teen Wolf.
When you upgrade the robot, it becomes Redbot, the character for the original test room for Reds (the codename for Broken Age)
The Grubbins use the same wording when referring to the kids, instead of calling them by name, in the same way that Linda does in Psychonauts
Wren can also join in with a costume of Surge Protector from Middle Manager of Justice
One of the costumes is Sweet Justice from Middle Manager of Justice. His special move is "sweet justice" and the Middle Manager theme plays when he initiates it.