Clean the walnut wood to remove any dirt as well as any residual wax or furniture polish. Apply a chemical stripper such as 5F5 or Zip Strip to remove the finish from the wood. Follow the directions on the package as to how long the chemical should be left on the wood.
Rub the walnut wood surface with lacquer thinner using steel wool. This will remove any leftover chemical stripper as well as smooth the wood.
Remove any stains that are still left on the walnut wood by applying oxalic acid. Lightly sand the area where the stain was.
Finish sanding the surface of the walnut wood with 220-grit sandpaper. Brush off the tiny particles left after sanding.
Polish the wood surface with walnut oil. You can substitute either linseed oil or a commercial product like Minwax Antique Oil.