Unless this is from a big camping trip or something... I can't fathom having so much laundry!
I'm weird. I think people have too many clothes and change them too often. However, if, for some reason, I ever had that much laundry to catch up on... nope, can't even go there. I wouldn't have that much laundry if ALL of my clothes were dirty plus towels, bedding and curtains! Here's what I *imagine* I would do:
1) Sort piles into each person's personal clothing, towels/bedding, other.
2) If towels/bedding are needed immediately I would wash and dry those first. Otherwise, I would wash a load consisting of one outfit per person (or 2 outfits if that made a decent sized load).
3) I would wash a load of bleached whites. If this included towels/bedding then I'd probably throw in any white socks and bleachable undies with that load.
4) From here I would seriously consider the loads I'm washing. What can be eliminated? I would have 2 towels per person and give away or store extras.
Since part of "catching up" would include drying, possible ironing, folding and putting away I would put the first load washed out on the line to dry. After washing and drying the second load I would bring the lined items in to dry in the dryer if needed. Those two loads would be folded and stacked to personal piles while starting a third load and NO MORE would be washed until those first two loads were complete.
I don't think I would endeavor to do more than 3 loads in a day and, after these first 3 loads were done, I would probably do one load per day to stay caught up.