soap - better than scraping yourself with a strigil

A detergent and soap are both surfactants, but soap is generally made from saponification of fats whereas detergents are generally synthetic.

Tallow is rendered beef or mutton fat.

Wax is synthesized from various plants and animals.

If you don't have soap, you can use clean ash or sand / soil as a substitute. (It seems like washing yourself with "soil" would just make you muddy, but perhaps that's better than being oily and smelly.)

Although there is evidence of soap usage as early as 2200 BC (a recipe was found on a clay tablet from that time period), it's use was not widespread.

The Romans' preferred method of cleaning involved massaging oil into the skin and then scraping it away with a strigil.

strigil