We had five kids and my stepmother gave us "chores" related to the washing, we did the fold/put on right person's "bunk" (bed) and that sort of thing, kind of like with dish washing chores.

My husband buys enough "sets" of underclothes (pants, teeshirt, socks) for himself to last X days so he knows when he has to do wash. All his socks are the "same" so he doesn't have a hard time matching them. Socks generally fit a variety of feet so I'd buy as many alike as I could so people could "borrow" someone else's or not. Does it make sense to do a female versus male wash day? I'd divide things up someway to make it seem less intense.