Rinsing with water gets a lot of the funk out. Detergent isn't good on your body, but if you wanted to get something like a shirt clean and smelling better a little laundry detergent to finish it off is fine. Sink is best place for smalls.

Body soap may have other additives depending on what you use that you don't want in clothes. Dr. Bronners is a pretty good all in one product for cleaning. People hiking the often use Dr Bronners for everything, including brushing teeth. check this article out