No need to get rid of toys. I had this problem and solved it with locked storage cabinets and fabric bins that can fit inside the cabinets. California closets or even the generic counterparts at Target will do the job.
I'd store all toys in these cabinets (at our house they're in the playroom and each child has such cabinets in their bedrooms as well). Big toys are assigned a home on a shelf in the cabinet, and live there permanently unless being played with. Sets or toys where there are tons of small pieces and parts like those little action figures and their accessories,Legos, Leapster 2 with all of its cartridges, etc. each get their own bin which also have their own home on a shelf that never changes. If necessary, for the children who can read, you can label spots so kids KNOW where to put things when it's time to clean up, and can find things when they want them.
Each night all the toys are picked up by the kids and put in the cabinets. Each day, each child gets to check out 3 things from the cabinet for the day. If they want something like Legos or action figures that has many little pieces, that's the ONLY thing they can check out. If they want they can trade an item for something else during the day, but the toy they're bored with must go back on the shelf. So with the exception of the daily checked out toys, I keep the cabinets locked and all toys in the cabinets at all times. Clutter has been greatly reduced and much more manageable.
Like you, we ask that toys remain in the playroom or bedrooms. Without the locked cabinets this wouldn't be possible. We'd probably find toys everywhere too. But with the limit on toys, it's a whole lot easier to track down the kid who is responsible for the toy that is found where it shouldn't be, and get it back to where it belongs by bedtime.
If you're wondering what to do with bigger stuff like ride on or scoot along cars, big Tonka trucks or things that won't fit on a shelf or cabinet, we lock them in the closet...to be checked out also.
Only parents and big kids (11 and up) can get access to the cabinets.
This has worked really well for us and saved our sanity. Our house looks good most of the time. Everyone can find their toys, and there are few missing pieces or broken parts.
When the cabinets get full, then we go through them and donate or give-away.
By the way, this week, Target has it's large California closet knock-offs on sale this week. We have these and use magnetic locks so the kids can't get in them.