When it comes to oil-based enamel paints, Wojtek is quite right. A lot depends on the actual colour, and how long the paint has been on the model (in terms of months or years, not days). Different pigment grains and gauges are used in different colours, and it is often impossible to totally remove all traces of a particular colour. The reason is that these 'grains' tend to separate from the carrier when the paint is dissolving, and 'clump together', leaving groups of tiny, almost invisible, patches which don't show until painted over again. This tends to happen most often around raised detail, crevasses, engraved lines etc, however fine this detail might be.
The caustic material will work, and one that Muller uses is a spray oven cleaner, called 'Mister Muscle' in Europe. I haven't used it myself, but I believe it works well.
Again, the colours involved can have a bearing on what is required. If it is acceptable to remove most of the paint, leaving traces which are streaks, rather than lumps, which can be sanded smooth, then this might suffice.