I only have a 3 yr old and a medium-sized house, and I still have trouble keeping up with all the little toys dispersed throughout the house. I've been trying to teach dd to put toys away when she isn't using them but she seems to have a different idea of what using them means, i.e. if it's not put away, it's in use. I think it's going to be a long while before I have my all clear surfaces back.
That said, four laundry baskets sounds like a lot of toys! Can you reduce the amount? Like, by half? (Or even more, lol?) If they had fewer toys, there would be fewer to leave around, and they'd be easier to put away too. How are the toys organized? Are they all sorted and put away by type? I used to try to do that with dd's smaller stuff, but I decided it was a waste of time, because they didn't stay put away for long, and because dd obviously didn't care about toy categories. So now she just has a drawer where all the little stuff gets thrown in together. Except for hair stuff and jewelry, I do sort that out, but we keep her toys to a minimum, so that's not hard to do.
I have a small wicker basket in the living room that I put toys in when I pick them up from around the main floor. When it is full, I go through it, get rid of the junk they won't notice is gone, and redirect the toys to their places (the playroom or the kid's rooms.) If I am leaving a room and there are big toys in it (the doll stroller, etc) I will take it with me (say, on the way to the basement) and deposit it in the playroom. If it gets messy in there, at least it is not part of my main living space so it doesn't stress me out.
Your four yr old is old enough to help put stuff back in her room. It does sound like a lot of toys though, especially for kids so young. If there are four laundry baskets full of toys they aren't looking for, I would seriously consider going through the baskets and donating things that aren't loved.
You might be surprised how much more they play with the toys they have if you get rid of the stuff they don't really love (the ones the inlaws have given, the crappy ones from party bags, ones from mcdonalds, etc)
I think the baskets are a great idea. I just think you need smaller baskets I have 3 kids (6, 4, and almost 2) our house is relatively small, we have a living room, kitchen, dining room, and our bedroom on the first floor and 2 bedrooms upstairs (2 boys in one, and girl in the other). The kids aren't allowed to bring toys into the dining room or our bedroom. So I have a small tox box in our living room for the youngest to keep toys downstairs since he's not allowed to go up and down on his own. All the toys that are on the first floor go in that box. If it gets full of toys from the older kids then I pick them out and have them put them away. When toys get brought into the kitchen I throw them back into the living room if they are left unattended. So usually a couple times a day I'm throwing random toys back into the living room. The toys that get left downstairs from upstairs go in a small basket on the stairs. When it's full I bring it up. The basket is probably only the size of a shoe box though. Anything that is too big to go in the box needs to be put away as soon as they are done playing with it.
It sounds like your biggest problem is that there are just too many toys. Maybe you could make a rule that certain toys belong only in their room and aren't allowed to come out. Your 4y/o is definitely big enough to start helping pick up his own toys and bring them back to where they belong. DD has tons of those little pet shop things, and mini my little pony's... she knows that those belong only in her room because there are just too many little pieces and if they come downstairs they will get lost or thrown away. If I have to ask over and over for something to get put back where it goes, then I put it away, right into the trash bucket. I'm sure it sounds harsh, but the older ones have learned real fast that way...lol I feel like if they are just going to leave their things around like trash, well then that's where they'll go. Obviously with a 1 y/o that won't work, and it's more about limiting the amount of toys that are available for them to bring around the house.
We also pick up every night before bedtime, downstairs and up. That helps keep the house tidier. I think having a good night time clean up routine helps, and I know I feel so much better relaxing after the kids are in bed with a picked up house.
I have one of these containers http://www.walmart.com/ip/Your-Zone-Pop-Up-Hamper-Grey-Flannel/13071860?sourceid=1500000000000003260370&ci_src=14110944&ci_sku=13071860 and I just toss any random small toys into it and set it in dd's room. It works out good for us. I get the kids to help me. They enjoy tossing toys in there. The one we have is pink/off white. I def. recommend a canvas one (like the link) vs. a nylon one. The nylon containers are flimsy imo.
As far as the kids picking through the laundry baskets of toys-how about picking all the toys up, putting them in baskets and packing them away for a couple months then when the kids are bored, bring out 1 basket. They'll think they're new toys.