Baking soda and water.

One tablespoon of baking soda mixed into a quart of warm water makes a great sponge bath. It cuts the body oils and wipes out odor. No need to rinse. You'll feel perfectly clean.

Hair washing: Find a container you can immerse most of your head into. Half-fill it with very warm water and two or three tablespoons of baking soda. Immerse your head into the water and rub your fingertips around your scalp, same as always. You may need a cup or something to dip up the water and pour it down from the hairline (while upside down). Then use a regular comb while your hair is immersed in the water, combing from scalp to end of your hair. You will prefer to rinse after this.

It really does work. Cheap, too.

Sue