On my big SAK, a SwissChamp, I open all the blades and tools and put it in the dishwasher. I try to position it so that it's in directly in the path of a waterjet. After the wash, when it's dry, I lube the pivots with oil.

For adhesive gunk stuck on blades, I use these products--one at a time, in escalating order: Purell hand sanitizer, nail polish remover, Ronsonol, and freon. Fortunately, the hand sanitizer works well enough most of the time and I don't have to go any further than that. I just have to wipe vigorously.