However you deal with the current situation, you need to consider how to stop it happening again once you have sorted it out.
I would suggest that any toys of the type that have "lots of bits and every bit is important", typically jigsaws, board games, packs of cards, etc. should be kept in the living room and never in a child's bedroom. They should only be played with under close supervision and packed away carefully after every use so that bits never get lost.
In the bedroom go all the toys that are not made up of bits, or where having all the bits is not important. A garage with cars can go in the bedroom, as the cars can be passed on separately as toys in their own right. A doll and dolls clothes, train tracks with trains, small-world house and figures, crayons and paper, Lego or other building toys, zoo or farm animals, books, all sorts of other toys can go in the bedroom and it doesn't matter about keeping track of every piece. These can then go to charity when no longer needed, as long as they are not broken or dirty, as each item is a toy in its own right, or 'enough pieces in a plastic bag' is fine even if some have gone.
It is the parents' (plural, including DH) job to sort and keep on top of toys, just as you sort their clothes. You have to train them to take care of toys just as you train them to put laundry in the basket.