K.,
Oh, how we all know the challenge of tornado clean up. I have three children, ages 9, 6 and 2 and I totally understand how you feel. First of all, I think you are ahead of the game by having toys belong in specific places, especially if they are buckets that have lids. We limit how many buckets can be out at a time. If all three kids are home, they get one bucket each. If it is just the two-year-old (while the older kids are at school), he gets two buckets.
If you are overwhelmed looking at a room with a huge mess, just think about how your little ones feel when they look at it. Such a task seems unrealistic to them. Our kids do much better picking up when we break down the task. For our two-year-old, we work with him to tackle one thing at a time. "Help Mommy put all the blocks back into the bucket and then we can have snack." "Let's gather all the books and put them in a pile by the book shelf." My six-year-old doesn't want help. He is a numbers kid. He has always loved numbers, so his instructions sound like, "Go down to the basement and put away thirty toys." (This sounds like a lot, but we have had to add to his instructions to start with the biggest toys first because he would scoop up 30 Hot Wheels and think he was done!) Our nine-year-old daughter is totally different. She is most concerned about cleaning taking up her time. Her instructions include a timer. "Clean up as much as you can in ten minutes." She loves this because it is a game to her to see how much she can get done and she knows it is only taking 10 minutes of her time.
Sometimes the instructions for all three of them are, "I'm vacuuming the living room in 15 minutes. Please put AWAY anything you want to keep." If a toy is still on the floor or is not put away (throwing everything on the bed does not work) then it simply disappears into the give away pile.
There are times that at the end of clean up time especially if I'm not about to vacuum, all is not cleaned up. That's okay with me.
We have also spent time as a family talking about fire escape plans and the older two know how important it is for the floor to be clear in case of an emergency. Their uncle is a fireman and this helps, too. He has explained to them how a fireman has to crawl on their bellies to look for people in a smokey fire. Your five-year-old son might enjoy playing fireman and the role playing could help him understand how dangerous all those toys can be.
Kids are so different. You know your kids best and will be able to figure out a strategy that works for your family. Whatever you do, make them responsible for their own mess!
I hope this helps,
T.