Nice face textures Airedale11! The way I animated the face textures for the eraser video was to create a series of flat planes, each with a different facial expression material applied. All of these planes were brought into scene mode and placed such that they all occupy the same physical space, slightly above the blank-faced eraser. In frame 1 of the animation, the "Visibility" parameter of each plane is set to off, or "0", except for the one which is the face that will be seen, whose visibility is set to "1". Through the animation, the facial expressions can be changed by switching the visibility of each plane off and on.
The only other thing I did was to use transparency maps to make the planes mostly transparent, except for the solid black facial features. This way I did not have to carefully match the colour of the face plane to the colour of the underlying object (in my case the eraser). Also, be sure to check that the planes are not casting shadows, or it will be obvious that the expression plane is slightly above the object beneath.
This method works for characters with very flat faces. For more 3 dimensional characters it might be easier to have a set of complete heads, each with a different facial expression, but still animated using the visibility function in the same way. Note that this method is limited in that the expressions do not morph from one to the other, but change instantly, which is fine for a cartoon-like project but probably not so good for a more realistic look.