First, come to grips with the fact that this is going to take all day. Second, split it up into two parts – clean the living area (by putting stuff “away” but not really cleaning or organizing) then on another day clean and organize the areas where things were “put away”.
Getting the kids to help can be easier than you might think. You have to set up most of this crap anyway, right? So each time you tidy up an item, set it up and let them play with it for a while. Play with them. Help them learn it so that they won’t have to ask you about such-and-such new toy every day for the next month. They’ll have had at least an introduction to all things Christmas-cool. And it breaks up the monotony of cleaning for you, too.
So, take a toy out, set it up, teach them how to play with it, play with them for a bit, then clean the surrounding mess while they’re busy. And when it’s time to do the next toy, make them help you finish tidying the first, and have them put it away before you move on. Get them in the habit of associating playing with new toys and cleaning up the toys when they’re done early on. Maybe it will stick. Haha, just kidding. It won’t. But we can hope.