We currently do two big laundry days, Tuesdays and Fridays (or sometimes Saturdays). Those are our clothes days. We do towels, sheets, napkins, and diapers in between but those are usually only one or two loads at a time.
So, we have one child who runs the washer, currently that's Ceili Rain. Josiah swaps the clothes from the washer to the dryer and from the dryer to the master bedroom floor. Then three kids who fold clothes. Zoe, Ace, and Liam usually will fold clothes when the littles go to bed that morning. I confess. Clothes some times do not get folded until the next day (or day after). But eventually, they get folded.
The kids clothes are sorted and put in their laundry bags. I picked these babies up online and had some awesome friends embroider the kids names on them. Love these bags!
The kids from Josiah up can put their clothes up on their own. Ceili Rain and Bryant are still learning and, honestly, I have not been consistent in teaching them how to do it. I'm getting there.
As far as clothes storage, we hang up their church clothes. The girls have one dresser they share. Two boys share a dresser and three boys share a larger dresser. So far, this has worked. As the kids get bigger we'll had to change our system (and when we add a third girl to the girls' room).