I've cleaned up a couple of 201s and didn't really disassemble anything that didn't just screw out easily. Both turned out well and hummed perfectly.
In contrast, I had a 66 that I bought for the cabinet. It was a refurb, so I decided to disassemble it and see what it would take to strip it and refinish it, as I have a Featherweight that will require stripping and painting to be nice. The 66 ended up going to metal recycling and the salvageable parts to a past member of this board. I realized it was a bigger job than I anticipated.
I also decided to part out the Featherweight, as the shop wanted $250. to disassemble it and reassemble it. I can buy a nice featherweight for $250. to $350., which is less than it would cost to refurb the one I have.
If you do decide to disassemble it, take lots of photos as you go. Put the associated parts in separate containers, so that things don't get confusing. Be very careful to keep every screw, as sewing machine screws don't match any other kind of screw.
I assume you have looked to see that the needle isn't bent, that's it's inserted correctly and that it has it's original throat plate. Other than those suggestions, I know nothing.
Given it's Christmas time, it may be a couple of days before you get someone knowledgeable about your problem.
bkay