For teeth....floss always. For 1-3 nighter, no brushing or paste. Longer stays, I've been known to make my own tooth brushes from green twigs...it works. My wife gets sample packs of tooth paste at her work. Soda works well too. Flossing is key, for me.

For dish/spoon, I sterilise with hot water and wipe dry. Generally use tortillas as my "plate" so there is usually nothing to wash. Rarely more than boiling water in the pot.

Body...if there is a lake/river/creek, I'll swim after sponging off. If I use soap, it will be Bronners, very sparingly. No deodorant....after a coupe days you can smell other hikers deodorant a hundred yards away. If desert hiking, I'm going to stink. You can only get so dirty.
TP...not usually. Plenty of 'natural TP' arround.