Fire and self cleaning ovens can warp old thin cast iron though many people claim good luck with it, I know of a few pieces that have been ruined. No I didn't do it.
Oven cleaner is just lye, it's caustic but has been used for years as oven cleaner and drain cleaner. I did use it before I had the tank and it works really well. I would try a self cleaning oven but I don't have one and most women aren't as tolerant of a house full of smoke and screaming fire alarms as I am.
And Pete be careful with that pee, it will eat the aluminum.