I believe the key with keeping toys organized is giving every toy a home. This way when the room gets destroyed it is so much easier to put back together, since you know there is a place for everything. Instead of going for the big toy box where everything ends up together, think about using smaller storage options to keep like objects together.
Here are a few example of inexpensive strategies for giving toys a home:
These little trashcans are so inexpensive and work great for toy storage.
Little plastic bins work well for holding cars and tools.
Baskets are always a favorite when dealing with storage, I pretty much buy all my baskets at garage sales for practically nothing.
This pop-up storage from Ikea works for stuffed animals.
I think this is a great way to teach young children organization and to be good stewards of their things. Remember, letting some toys they no longer play with go to a new home will also help this area!