I use shampoo, either wearing my clothes in the shower, handwashing or in a washing machine.
Make sure you take your cell phone out of your jersey pocket first! Don't ask me how I know this.
I usually take 2+ sets of bike clothes. Depending on the possibility of cool weather I will add a long sleeve jersey or two if I know it will be cold the whole tour.
One set is rinsed at night and dried. Hang on bags in morning if still not dry.
I have off bike clothes too. I usually take 2 pair of pants and 2 or 3 jerseys / tshirts. I use those pants that zip off at the legs so they can double as shorts.
I'll take a comfortable pair of shorts for sleeping and wear them when doing laundry on longer tours.
If I know it is going to be warm I just bring a pair of sandals that double as shower sandals. If it is going to be cool then a light weight pair of shoes. Gives the bike shoes a chance to air out.