I just went through the same thing after buying my first home, a definite fixer-upper. The previous owners had painted over the hinges a number of times and it was a giant pain to get the hinges off. I sprayed the hinges with Goof Off, an adhesive remover that also works on latex paints. I kept spraying the hinges and especially the screws until the gunked on paint had softened enough that I was able to brute force the screw. In only one case did I have to drill a hole into the screw to get the screw out.
Once the screws were out and the hinges removed, I sprayed Goof Off over the area and used a small (3 inch, maybe) putty knife to scrape off the excess as much as possible. Once the paint was as smooth as I could get it with the adhesive remover and putty knife, I waited for the paint to dry (from the Goof Off). Then I used a small power palm sander to sand over the remaining ridges and bumps to try to get it smooth before repainting.
I am still in the midst of this project, but this was how I was able to get the doors and hinges off of my old kitchen cabinets. I'm planning to repaint the cabinet interiors (which are a very dark and dingy muddy brown) and cabinet face a nice bright white, and then to cut out beadboard (from the large 4 x 8 foot panels) to reface the front of the doors. The doors will also be white (kitchen enamel paint from Lowe's), and I have new brushed satin cabinet pulls and knobs. Hopefully it will look far better than the previous dirty cream and fire engine red!