Stripping paint seems to always be a messy project. To some degree, it depends on what you plan to do with the trim after the paint is removed. If you are planning to repaint or "wash" with a color, then a little old paint in the cracks and crevices won't matter or may even add to the look. If you want a pure wood finish, you have to get in there with small tools and brushes to get every last bit of paint out. I like the gel strippers...used to be one called "Wonder Paste" (? I think??). There are similar ones still sold today. Another option is a heat gun.
I'd sand it off before I'd ever use a stripper.
A picture of what your dealing with would be a big help.
Any properly painted trim even when it's new should have three layers on it primmer and 2 coats of Paint, so I'm thinking there's more to this story than what's been said.