I've read the comments and I've read your original post and your ETA. Your toy division system makes sense - if 1/4 of their toys is a reasonable amount and not 100 toys. I'm assuming the division of toys is somewhat logical too, so that various sets are not broken up to the point that they are rendered useless.
I think you need to define "special time" toys but maybe you have in your own mind and with the kids.
I don't understand at all what you mean when you say if you tell them they won't get lunch, they will not only skip lunch but also dinner and go to bed hungry. That's absurd. And they don't care if they have no toys? What happened when they lost them all? Surely they did something all day besides sit there. I think you must be getting too impatient to what it out or to let them have some consequences. I'm guessing you're showing your frustration, and you're getting up and either sweeping things away in anger or you are picking them up yourself because you can't wait for them. The kids know that they just have to sit there for a few minutes until you give up and give in. It might seem like an eternity to you because you are impatient to move on to the next activity or chore or errand.
You say that your child listens in school. So he's capable of doing this. There's something unclear in what you are saying, expecting, or doing. Do not put the child's hand on the object - the child is completely passive that way. Get him to pick it up. (Or, "Can you find the red truck?") Then: "good job. Now can you put it in the truck box?" then "Good job.")
You can't take away privileges at this age - you can't say "no TV tonight if you don't pick up toys now." Kids are "in the moment" and don't defer well at this age. So sit them down, look them in the eye, and CALMLY say what you want done. Not "clean up" (too vague) but "put the cars and trucks in the box with the car picture on it." Ask them what they want to do next, or comment on what you see them doing - they want to go out, or they want to get out the art supplies? Fine. Kid A: Put the cars in the car box. Kid B: Put the books in the book holder. That's all the do. Nothing else. When it's done, compliment them and let them do the desired activity. If they say, "I want to watch TV" (or whatever the activity is), your answer is, "I know you do. As soon as you….then you can watch." As others have said below.
Is your clean-up system obvious? Not to you, but to a 3 year old? If their toys are in a huge pile on the floor and they have to put them in a huge pile in a bucket or on a shelf, maybe they don't see the difference? I had a couple of buckets/bins. I put a picture of a car & a truck on one - that was for all the vehicles. I put a picture of a stuffed animal on another - so all animals went there. Do this for whatever categories they have the most of - could be action figures or building things like blocks and Legos. Either print a photo off the internet, or cut out the front of the box it came in, or take a photo yourself of the actual toys lined up, and post that photo on the bin. I had a divider from the office supply store on the shelf that allowed for books to be inserted so they didn't fall over - nothing is more frustrating to a small child than trying to put books away and have them slide and tip.
I think you may be asking/telling in too many different ways. There has to be one set of 2-3 commands/sentences every time. And you have to stick to it. What doesn't get picked up gets taken away. How do they get it back? By picking up what they have - in a simple and organized set of instructions, 1 at a time. If you take stuff away, how have they gotten it back in the past? Somewhere, you're giving in.
There is no child who will sit in an empty room and refuse food for hours on end. Somehow, there is something missing from this story - the children are getting some sort of a payoff for refusing. Find out what that is - it could be that you give up, or that you start cleaning yourself, or that you are just so efficient at picking up and pitching things where they go that the kids are overwhelmed by the frenzy. But there is a reason they don't have to mind you - so find that.