What methods can I use to remove exterior paint from brick?
This all depends on how long the paint has been on the house and what kind of shape it's in.  Because brick is a porous material paint adheres very well to it.  I think your first step would be going to the local paint store and rent a power-washer.  A gas powered power-washer.  You are going to need as much psi as possible (at least 3000+) with a pin-hole revolving tip. This will blast away any paint that is loose on the brick. 

This should be less damaging to the brick and mortar than sand blasting.

Depending on how successful this was in removing paint dictates your next steps, if most of the paint is gone, then maybe just a wire brush and some paint remover will get the job done.  If you've power-washed your whole house and it is still covered in paint, then I would call a contractor and get quotes.