bowlegs: I stay clean (& mostly odor free) on my hikes by taking a head-to-toe towel bath every evening before hitting the sack and by carrying a clean sleeping/town shirt.
I typically heat up a pot of water & add about 20 drops of Dr. Bronners soap. I use a real washcloth (vs bandana, which isn’t nearly as good) to wash with and it doubles as a water bottle cooler for the desert sections (evaporation cooling effect).
Another tip: I regulate my hiking speed according to body temp so that I don’t sweat too much. When its really hot I dip my shirt in any available water and either put it back on or flip it over my shoulders & back - which is kinda like hiking shirtless, but with the added benefit of cooling on the skin that’s in contact with the backpack.
Final tip: I carry a frame-less pack (MLD Prophet) which means I can wash it with my clothes in town.
I have often been called the ‘cleanest thru-hiker on the trail’ on my various hikes - no doubt due to the towel baths and other strategies. (I also normally carry a tiny thing of deodorant.)
I do laundry every time I hit town.
I hope this helps!
freebird