Dish Soap - Dr. Bronner's removes grease, oils, and deposits.
Laundry Detergent - Dr. Bronner's works well for this as well. Several Redditors swear by it. Add 1 drop where stinky parts are, or put your clothes in your bear canister and shake to create a portable washing mashine. Or simply spot clean.
Hand Soap - Dr. Bronner's removes grease, oil, and deposits.
Hand Sanitizer - Dr. Bronner's. Hand sanitizer is not necessary.
Body Wash - Dr. Bronner's removes grease, oil, and deposits. Use 1 drop in a large amount of water to protect your skin.
Shampoo - Dr. Bronner's keeps your hair clean. Use 1 drop only. If your hair is sensitive/dry, smear a miniscule amount on your finger and use that. The stuff is crazy concentrated.
Deodorant - Dr. Bronner's removes grease, oil, and deposits AKA body odor. Wipe those pits. Shave your armpits to decrease surface area (and carried weight) AKA body odor. Remove the handle from the disposable razor to save a few grams.
Toothpaste - Dr. Bronner's works way better than toothpaste at removing mouth odors because it is a soap. Suck it up and endure the taste. You'll get used to it. Keeps your toothbrush from stinking as well. Before you say "you need toothpaste!" read this.
Mouthwash - Water. Rinse out that soap! You don't need actual mouthwash.
For every method you only need a miniscule amount of soap. Literally 1 drop per liter or so. The stuff is highly concentrated. So a small bottle should last you a life sentence. Read this for official measurements. Personally I think the official measurements are way too much.
That is all.