Best solvent for hardened oil is isopropyl or ethyl alcohol (better than mineral spirits, pb-blaster and acetone) and it won't eat the paint and plastic; caustics will also eat paint and attack non ferrous parts. I have a hardinge TM horiz mill that I had to soak the dial lock-nuts in for hours in warm IPA to unfreeze them. Still, I would avoid soaking the plastic graduated dials for a long length of time. I think that sliding ring has a ball or ball-end detent that may be stuck in its hole, in addition to any gunk on other areas (seems I recall slightly modifying that on the tailstock of my lathe at some point).
I also have a mid-80's HLVH-EM, and have taken the geared dials completely apart; it is not difficult, however all the parts are extremely close-fitting and you have to make sure there are no nicks, burrs or grit, and align things carefully during assembly. There are also a couple of spring-loaded shoes in the dials, so make sure those don't get away from you while disassembling the dials. I also ended up putting thin lock-nuts on the existing outer dial lock-nuts, as I got tired of those nuts moving slightly and messing up the play and feel of the assembly.
Another thing that gets stuck with polymerized oil are the bushings for the selector knobs, and feed/thread knob. The bushings are pressed into the housing, and the selector shafts are very close-fitting in those bushings. These can be freed up by taking the knobs off, dousing the inside and outside of the shafts with alcohol, and working them axially (with the couple mm allowed), from the outside and inside thru the gearbox covers. Cheers.
