If you don't have a toothbrush-

The goal of brushing teeth is to prevent tooth decay. Prevent tooth decay by preventing bacteria buildup on teeth. Plaque (the slimy film that appears on teeth after a day or two) is a buildup of bacteria, saliva, and tiny food particles. If you can remove this once or twice a day, before it becomes hard (tartar) you are much less likely to have cavities and gum disease.

You can do this without a toothbrush by taking a small piece of rough cloth (like the corner of a washcloth or towel) and rubbing it all over your teeth twice per day. Rinse it well afterwards and let it dry completely (preferably in the sun) between uses.

If you don't have toothpaste-

Toothpaste is a paste containing rough particles, flavorings, and other chemicals that remove and may help prevent plaque and tarter from forming.

If you're doing a good job brushing your teeth to disrupt that plaque formation, you technically don't need toothpaste. However, if you would like a little bit of freshness or feel like you need more than just a brush or cloth, you can take a pinch of baking soda and (optional) add a drop or two of flavored extract (like vanilla or peppermint- DO NOT USE ESSENTIAL OILS FOR THIS). Put this on your toothbrush or cloth and brush as normal.

If you don't have deodorant-

Deodorant is not absolutely necessary for health, but if you work somewhere that has a "hygiene code" or some BS you probably need to smell like something other than a human.

The recipe is the same as toothpaste above. A pinch of baking soda and (optional) a drop of extract like vanilla or peppermint. Rub under each armpit.

If you don't have lip balm-

Lip balm is often necessary in colder or dryer climates to prevent cracking and infection. Any fat can be used as lip balm, for example, petroleum jelly (Vaseline), lard, butter, vegetable oils, your own face grease, etc... Just put a drop on a finger and rub on your lips until it rubs in.

If you don't have toilet paper-

You will need a plastic cup and a wash cloth. Use the plastic cup to pour water over the soiled area. If it's poop you'll need to use your hand to make sure everything washes off. Once clean, use the wash cloth to dab up any remaining water. Wash your hands well afterward.

This might sound horrible if you're used to toilet paper, but it is used all over the world and leaves you a lot cleaner than TP does.

If you don't have soap-

For handwashing- use water to wash anything visible off the hands, then follow with hand sanitizer or a few drops of rubbing alcohol to sanitize.

For body washing- You don't actually want soap for most of your body, including your privates. Wash with water only. For hair (since it tends to look greasy if unwashed), use a few teaspoons of baking soda or tablespoons of lemon juice and rub it in. This will help get rid of dirt and grease when soap or shampoo is not available.

If you don't have nail clippers-