From several past expirences, this is a though job. Oak is an open grain wood, look closely at it and you can see small "channels" that run the direction of the grain. Getting the paint from these channels can be a challenge.
I personally believe that a Methylene Chloride stripper will work the best. Sodium Hydroxide strippers(Like Peel-Away) tend to darken hardwoods like oak leaving you with surface that won't take stain well. On a past project, we used brass wire bristle brushes and a stripper called "Circa 1850" (made by a Canadian company called "Swing") to scrub most of the paint from the grain, from there we used picks like the one your dentist uses to gently dig out the remaining paint. It took hours upon hours to finish. As DH suggested, you might take one of the doors to a person who does "Dip Stripping". One door shouldn't cost that much and it may be worth seeing how well it does the trick.