I don't think throwing away toys (unless broken or missing pieces) is ever a good idea even if it is because they won't pick them up. It doesn't teach them anything. They won, you were the one who took care of the mess and they didn't have to. And honestly, for those kids who I know are allowed to destroy their toys or their parents will just throw them away, I don't buy toys for them any more. In fact, I did not buy one single toy for Christmas for the 4 kids I usually do.
It sound like this is not the first time your kids have not cleaned up when you tell them to, is it? I know with boys it is very tough, I have a boy who just turned six. He is 100% responsible for his room, toys, making his bed and his clothes. And he has been for over a year now. You need to be more in control, they are running all over you.
First thing to do is get a book called "To Train Up a Child" by Michael and Debbie Pearl. I don't know if you can get their books at stores but go to www.nogreaterjoy.org. What I did is make every toy has it's place, he has several totes in his room and they are all organized, cars are in one, transformers in another and so on. DO NOT let them have free reign in their room until they are totaly trained. What I did when he wanted to play with toys is bring 1 tote to the living room and he was able to get 1-2 toys out at a time. Before he could get out another toy, those got put back in. If he wanted a different tote, that one got put up. When I said it was clean up time, all the toys and the tote got put up. When he was following those rules and developing new habits, and also realized he was responsible for keeping his room clean and there were consequences for not, he did not make his room a mess. Also, when we were in the training process, and I said it was clean up time, I stood over him. If he started playing, there was a consequence, if he started doing something else or tried to walk away from it, there was a consequence. Don't tell them to clean up and then leave the room.
You'll get it, but they need to be trained. Good luck.
www.ReflectionsByAmber.etsy.com