Need answer fast? 
Perhaps there was some sort of cloth covering on the cage and they asphyxiated? (assuming a normally breathable cloth can smother if saturated)
Maybe the water made them dissolve.
The wedding invitations were produced with some inexpensive glue that was known to be toxic. Plus, it didn’t stick very well so you had to put a lot of moisture into them
I don’t remember, but I also don’t think they were in NY. Isn’t Miss American held in Atlantic City? Plus, even if Jerry was cold, they were still sleeping with the screen door open, it couldn’t have been that bad