Well, if there isn't a lot of design detailing on the doors, the fastest easiest way I've found to remove paint from flat surfaces is with something called a "Nestor Scraper", named after it's inventor, yours truly.
To make a Nestor Scraper, you simply grip a single edge razor blade
in the jaws of a pair of needle nose style locking pliers
and then dull the blade in a belt sander (or on a piece of fine sandpaper. You want to dull it enough so that it won't cut into the wood at all. The duller, the better, but try to dull the blade evenly.
Now, use a heat gun to heat the paint in front of the scraper and just shave it off the door. When I do this, I typically shave off all the coats of latex paint in one pass, and then go back and shave off all the previous coats of oil based paint. Latex paint softens up more than oil based paint when it's hot, so that I can tell which is latex and which is oil based.
In your case, I'd spend the extra money and get a good quality heat gun with electronic temperature control so that you can turn down the heat setting so as to avoid scorching the wood. Cheap heat guns only have two settings; Lo and Hi, and the Hi setting will leave scorch marks in wood. Low works better, but it might not be hot enough to allow you to work fast.
I highly recommend the Milwaukee Model 8978 heat gun:
It's light enough that you can hold it in one hand all day without getting sore wrists, it's shape allows it to be propped up at the back so that you just have to move it forward as you work and it'll blow hot air onto the surface you're working on, it has 6 temperature dial numbered from 1 to 6 with a stop between each number for a total of 11 temperature settings, and a variety of accessories are available for it, including a concentrating nozzle.
You will find that your razor blades will eventually stop working properly and want to cut into the wood on one side or the other. What's happened is that the metal blade has warped from the heat, and you have to dull a new blade.
If you're planning to repaint the doors, I'd recommend you use an INTERIOR ALKYD PRIMER and an INTERIOR ALKYD PAINT on them. Doors take a lot of wear and tear, and you want a paint that dries to a hard enough film to stand up well on the door.