I totally feel your pain, as it sounds as overwhelming as what I went through a few years years ago when we moved out of our children's first home (my oldest was almost 8, at the time)! We had a TON of storage space, so my tendency was to keep, rather than throw/give away. Let me tell you, I vowed to NEVER do that again! Once you go through the process, the memory of it with be a great motivator!
You have gotten some GREAT advice so far -- you will be surprised at how your children respond to being involved -- at the very least, much better than the reaction you will see once they discover a "treasure" mysteriously gone! The idea of "rotating" toys is a great one, too, as it will give you the opportunity to wean out the outgrown toys more often.
As for organizing of the toys they do play with, do you have room for a few book shelves? Although they aren't the greatest "quality", I've picked them up pretty cheap at Shopko (I'm sure you could find them at Target or Walmart, too). Then, buy baskets to keep "like" items in, Barbies and all their clothes & accessories (keep small things, like shoes, etc. in a zippered pencil case), match-box cars, etc. For legos, I've always bought clear bins with lids - when they get a little older and have the "kits" you can keep the instructions in there, as well - no need to have a bin for each kit, though - just a large enough one to fit a whole mess of the things in.
This system will cut down immensely on toys being strewn all over the place, and minimize the risks of losing pieces, etc! You just teach them to take one basket out at a time, and put everything back in the basket & back on the shelf before getting something new!
Good luck! You will be soooo happy to complete this project!