How easy is this to do?
I'm asking as I was thinking recently that my headless would look awesome with an oiled wood finish...
It depends on what the finish is and how well it was applied, sometimes it is very easy and other times it is frustrating. Some people use chemical stripper which makes it much easier but I prefer sanding on a guitar especially with something that you don't plan on repainting as the stripper may stain the wood.
I'm talking about effort here, as far as how complicated it is, it's not. Removing paint is simply a matter of labour, time and patience.