My advice is don't start spraying solvent all over the guts. It's not needed. Varnished oil doesn't cause any problem on the middle of shafts, etc.
I have never had to remove wiring to free up and lube a machine.
You only need to use DROPS of solvent (kerosene, alcohol, kroil) where there is metal to metal contact (bushings, pivot points, gears, etc). I use the same flip top bottles we use to carry alcohol for camping stoves for kerosene and alcohol.
If you just have to pretty up the shafts, use a strip of cloth with solvent and use a shoe shine motion to quickly remove the varnished oil.
On the outside, use rags or cotton balls wetted with mild solvent and clean small areas at a time.
You are working on sewing machines....loose the engine cleaner/power washer mindset.
What I did was put 99% Isopropyl alcohol in a spray bottle and sprayed all the guts liberally. I used the pressure from the spray bottle to blast off all the old semi-dried grease from the nylon gears. Worked pretty well and I turned the hand crank and sprayed again. It worked as I could see the discolored alcohol coming out on the towel. Then I applied lithium grease to the nylon parts and reoiled the machine. It feels much better.
That was the white machine. Next is the Necchi.
It looked like thats what was on it prior. It was all dried and caked like lithium grease tends to do with age.
So I should have just oiled it instead? I do have sewing machine oil.
All kinds of things get put on sewing machines. My niece used Pam cooking spray for a while. Took my brother in law forever to get that machine working again.
I think the thought was that no one knows what the long term effect of automotive greases on the old plastics might be. I'd just clean it up and re-grease with the tri flow or singer sewing machine grease months from now when it needs greased again.
Also, Lithium grease is basically just soap.