As for people giving me stuff...they've pretty much stopped.
There is a joke that "you better not give Sara anything...or you'll see it on eBay".
Somewhat true. If they truly know me, they would stop giving me crappy stuff anyway. But it's the thought that counts of course...so most of the time I will graciously accept the gift...and then freecycle or craigslist it. My MIL has come to know me well...she will bring me something and say, "ok...tell me if you don't like this". At least she gives me an out.
Anyway. On to the toys. Your kids will play with whatever is there. They may whine or be mad for a bit...but maybe you can get them involved? Can they help pick toys to donate to other kids? I know it's different for older kids...so I can't really give advice on how to help them adapt. Basically, if I don't like a toy, I just give it away and Bella never notices. Most of the time, it's ME having the trouble getting rid of something because I'm the one who thought it was such a cool toy. For me, the key is finding toys that are compact or can shrink down. She LOVES her playsilks. I think I have 4-5 of them and they shrink down to nothing. But when she's playing with them, they are huge and extravagent. We have nesting blocks, small wooden blocks, soft cloth dolls, small musical instruments. It's all small...and it works.
I know their are tons of threads on toys...you'd probably find some great ideas by searching on that. Congrats on continuing the decluttering!
Isn't it addicting!?