N.S.
Don't know how much space you're dealing with, or if you're on a tight budget, but my number one favorite piece of advice for this problem is to invest in a number of "tall and deep" storage cabinets that lock. If you get them without locks, you can use removable or magnetic child safety locks (for safe proofing your home).
Thanks to California Closets and it's many discount store knock-offs, and space saving furniture stores like IKEA, you can have your nightmare realistically under control in one weekend. And with style. There are fashionable cabinets in all price ranges and at most stores. Just decide how many cabinets you'll need to house your toys. Be sure to purchase some bins that can fit inside to hold small loose toys. And purchase locks if you get cabinets that don't have them.
Devote one weekend to sorting and organizing the toys by child and toy-type. I highly recommend getting rid of toys they don't play with, or are missing parts. Realistically, if you haven't found the parts while cleaning the house, they're probably gone for good. Be sure to check with your children before you send the toys on their way. But don't let your children bamboozle you if you know they don't really care about the toy and are just being clingy. If you tell them they can sell the toys for money, or that some other child might enjoy it more, they might be more willing to part with them. Be merciless.
Once you clear the clutter and get the toys under lock and key, the rest will be up to you and the kids to work out a lending library/check out type system for accessing the toys. The good news is it's easier than you think.
This is what we've done at our house, and it's wonderful. Our clutter is very little, and the kids are much better at taking care of their toys and managing small pieces without my help.
The cabinets are organized by kid, and toy type. I use bins inside the cabinets to manage the toys, and have certain shelves resolved for bigger stuff like playsets. We dedicated an entire wall in our playroom area to an IKEA storage system, and two smaller California Closet-type cabinets in each child's room.
Each morning "each" kid can "check out" 3 - 5 items for the day. Once they pick their toys, the cabinets are locked. If throughout the day, they decide they want something else, they can trade one or all of their morning items. They can only have a maximum of two "check-outs" to cut down on my having to spend the entire day guarding the cabinets. Between each kid, they have more than enough stuff to keep themselves entertained for the day.
While the method doesn't totally eliminate messes, it greatly, I mean greatly cuts them down to size. Each night, right before bed, each child has to "check-in" each thing they took out for the day. If any pieces or parts are missing, the whole family goes on a recovery mission for the missing part/parts. Kids are responsible for keeping the shelves in good order, and at least monthly, we clean them out and remove any toys that they don't want to play with anymore, and we put them in a box and take them to Once Upon a Child (a consignment chain for kids toys and clothes) or the Goodwill. Any money we collect for a toy from consignment goes into their toy budget/allowance bank to be used for something new that they want to buy.
This system has been a real life saver for us. I devised this while I was on total bedrest with my last pregnancy. I couldn't afford to have big messes since I was dependent on others to manage the house while I was down for the count. The plan works so well, especially in helping little kids manage their stuff, I can't say enough in how it has been a life saver and a new way of life for us.
I'd like to add, for things like stuffed animals, we purchased one hanging mesh storage tower for each kids' room. You can get them at IKEA for $5. The animals are accessible, yet out of the way, and taking up very little space in the room. They also aren't that bad looking either.
If you don't have an IKEA in your area, you can order their entire stock on-line at www.ikea.com