I finally took the time to do a search. I figured laundry was not a popular topic with backpackers but people are indeed inventive. I am considering putting my clothes in a stuff sack, filling it with water and soap, sealing it, then squishing it for a few minutes. Then, I'll wash out the soap somehow. I haven't figured out how to dry it yet as I am constantly on the move.
Would Dr Bronner's work well for this?