A bunch of crumpled green straight leaf grass + sand will do the dishes pretty well (removing crud and grease). Bacteria? What bacteria? Just wash it right after every meal, rinse and let dry preferably in the sun.

For the laundry the best ancient method I know is trampling clothes in a bathtub (some detergent needed though). Clean clothes and clean feet - guaranteed.

Proven hair shampoo:
make 2 tbs of powdered oatmeal, stew it with boiling water, add 1 fresh egg yolk (optionally add 1 tbs of honey). Massage this dough into the hair, let it dry for 15 minutes, rinse.

Weekly body wash - make yourself a sauna. Use a bunch of fresh crumpled grass as a sponge to scrub the skin when sweating starts.