What is the best way to polish or wax solid wood walls?

Use Murphy's Oil Soap or Bona for wood.

Milsek.com I use their cleaners and am very happy with them. No wax build up

This may sound strange . . .but try Mop & Glow for floors. This product hides a multitude of sins and really leaves wood shining. With no traffic on your walls (I’m guessing) the wax should last a long time. I would use something like a flat swifter mop head to apply.

https://www.wikihow.com/Clean-Wood-Walls

I use Old English for all my wood cleaning and it really is good for the wood. It comes in dark or light and cleans it at the same time. Find it where furniture polish is found, but it is good for ANY wood

if you plan on using peel and stick hook hangers...for art work, dont wax the wood. it wont stick on a waxed wood. i have 3 rooms with that treatment. learning to hate the stuff.

I had wood walls in one bathroom and used liquid gold on them. Wax will build up. I apply the liquid gold and then wipe any excess off.