To stir means to move something (a spoon or electric mixture) in a repeated motion to combine a number of things together.
Mix means simply to combine different elements together. It might or might not involve using a motion of a tool to do it. I could mix languages together. It could be real physical mixing or intellectual mixing.
To whisk means to stir with a fast motion using a wire mesh. Some cake mixes or other recipes require this. [Note: whisk also means to wipe something away with a quick motion of the arm.]
To review: If I whisk to combine things, I am stirring and mixing.
If I stir, I am mixing, but not necessarily whisking.
If I mix, I may be stirring and/or whisking, but not necessarily.