We have the same problem here too. Our solution is to save what we can by taking it apart and hopefully reusing it again. If no one remembers what show it is from (the program is student run, so a limit of 5-6 years old), then we toss it.
If there's a chance you're going to use them again, look for a storage facility that is perhaps outside of your school. Problem is, this will cost $$$ and lots of time to move everything out.
You could also look into some "Pods" or steel shipping containers to put scenery in.
Also, another time consuming task is to take everything apart and store the pieces if you can. Or just the pieces you want.
Or post the set on ebay
