Weeeelllllllll, for gunky parts like that I use:
Sewing machine oil, but that doesn't usually clean the varnished oil very good, so then I go to -
Denatured alcohol as it cuts the old varnished oil and evaporated quickly, but it doesn't always work, so then I get out the big stuff and use Hoppe's #9 gun cleaning solvent. That has not failed to do the job.
I use q-tips, cotton balls, soft cloths and tooth brushes. I do not use steel wool because the steel fibers can get stuck in parts of the machine and jam it up. Also sometimes those steel wool pads just disintegrate and you have a nasty mess.
I am not a restorer so I don't always want them to shine like a new machine. I just want them clean enough to work properly.
Joe