To clean fine wood such as a bannister in oak or mahogany, go carefully. Mix 4 parts white spirit with 1 part linseed oil. Apply with a cloth.
Only if you really have to should you use 000 grade wire wool. Go gently and with the grain of the wood.
Then wipe with a clean cloth and white spirit.
You could just remove worst of the grime - leaving a bit to reflect the age.
Wax can be removed with methylated spirits.
To clean exposed beams, you can afford to be a bit rough. Use a scrubbing brush with washing up liquid to clean them. When they have dried, use a coarse sandpaper to remove the splinters, finishing off with a medium grade paper. You are not trying to achieve a 'cabinet' finish. To finish them, you have two choices. Black paint was used in the Victorian period, but if the beams are not already painted, go instead for some brown stain to even the colour (if you need or want to), and then buff with wax. Don't use varnish.