Sounds to me like it's time to get tough. If they have the ability to put things away, and it sounds like they do because you are expecting them to do things, then hold them accountable.
Like you said, you're buys cleaning and they're just doing nothing - problem. They seem to think that if they leave it long enough you'll clean up for them. Time to play hard.
Two options - firstly, is there anything fun thay you guys had planned coming up? An outing, or a play at a friend's house. Simple - they don't get to go until their bedrooms pass inspection. You don't need to nag or shout, just keep telling them to go back to their room and get cleaning if they want to do the fun activity. Don't back down, they'll test you to see if you give in. No tidy room, no going anywhere.
Second option, for when option 1 isn't working or isn't practical anymore. Tell them that their rooms need to be tidy by 3pm on Saturday (or whatever). At that time, tell them that you will be coming through and picking up everything on the floor or not in it's place. Tell them that if they can't take the responsibility to put it away, then they obviously have too many toys. Again, don't nag and shout, just tell the kids to keep tidying because you'll be in in 1 hour/ 45 min/ 30 mins etc to collect all their 'unwanted' toys. When you collect them, you can either put them in a box and put them away for a month or even three months (it needs to be a good amount of time) or - and this is what we did in our house - take the toys to the op shop. Only had to do it twice, now the threat is enough because they know we will follow through.
After these two op shop trips, if things get bad and everyone gets sent to his/ her room to tidy, I tell you what - the job gets done by the allotted time. The only thing you have to check before you make this threat is that any special toys like cuddlies, books from Grandma, expensive Christmas presents etc, thing you couldn't bear to part with are put away. Sometime I spend 15 or 10 mins with the kids first to get them started, then leave them to it. Make sure you get them to put anyway any of these toys first (or put thesein a cupboard for a few months).
These are pretty firm, but it sounds like the issue isn't tidyness, it's the kids not cleaning up when they're suppose to. Hope this give you some ideas,
Libby