To get around those hard to get to areas, try pushing sandpaper strips
across the areas with a small wooden implement.

For small areas that you can't get any real movement that have finish
buildup, try your Dremel tool with the appropriates set up.

On the other hand, you can do some good removal with a homemade
scraper. Cut down an old steak knife into a thin, flexible shape
(grind off the cutting edge!) and use the tip to get into hard to
reach places. These can be found anywhere and can be ground easily to
a useful shape.

To see what kind of finish you have on the wood, you can use the old
"rule of thumb" on a place where you won't see your test. Make sure
you do this in an area that hasn't been waxed, oiled, preserved or
anything else as it will screw up the test.

The following is considering you were talking about clear finsihes.

This works pretty well, but isn't a perfect test: On the wood, put a
large drop of anhydrous alcohol. Next to it, put a large drop of
lacquer thinner. You may need to add a drop now and then to keep the
surface wet. Give it a couple of hours to work on the surface.

If the shellac drop gets gooey, you have shellac for a finish. You
will have further proof if the drop of lacquer thinner does nothing.

On the other hand, if the lacquer thinner side gets gooey, you have a
lacquer finish. If both sides get gooey, some wise guy got cute and
mixed them.

In any event, both of these finishes are easy to sand down and can be
easily top coated with more of the same.

If neither of those dissolves the finish, you may have varnish or
possibly polyurethane. If the piece is old, you probably don't have
polyurethane.
If you have varnish you can Google "varnish repair" and "varnish
removal" and you will get all you need to refinish.

Robert