Here is a blog detailing how to dismantle a 66:
http://mysewingmachineobsession.blog...66-or.html?m=1
These machines are extremely simple compared to even machines from the 50's, so taking one down and putting it back together will be easy as long as you are patient and take your time.
For your problem I would start by taking the handwheel off and see if paint worked into the rear bushing, as I imagine that would be the first place paint might seep into if it was not masked.
If paint is visible there, scrape it off with a razor blade or dental pick, or very carefully apply some paint stripper with a q-tip.
I would also make sure oil visibly lowers into the oil holes along the top. If they do not, they are likely plugged with paint.