Braving the sniping...
Perhaps it should be pointed out that the first post asked how to get out of deploying "legally." Now, there could be long arguments about how legality interfaces with ethics, etc. but perhaps a more pragmatic approach would be useful. People have been "dodging" orders for ages quite legally.
"Hardship" was mentioned. Well, if you have a case to make that you qualify for a hardship exemption then make it. No harm there as long as you don't lie on your application. The military may or may not approve your request, depending on the circumstances.
"Braces" and such is a more difficult question. If you need a medical procedure (i.e. advised by a doctor) that disqualifies you, then so be it. However, there are probably rules/laws against having *elective* surgeries that disqualify you. Thus, if you really need braces (and have just put off getting them for some reason) and can get a Dr. to certify that you need them, you could do that. However, if just get them and don't need them you could line yourself up for a world of hurt [ myself, I'd prefer a tour in Iraq to dental torture... ].
"up and out" is an age old tactic. Basically, you sign up for some career enhancing/vital skill or school that gets you out of recall. Commissioning programs are famous for this. Sign up for ROTC. However, be mindful that if you sign for more obligations you may just be getting yourself in deeper. The Army/ Guard may or may not approve of such a move. You could also agree to study something like Arabic or Islamic Studies to help make your case for staying more powerful. HOwever, if you acquire a 'vital' skill it will make you that much more in demand later down the road if you still have obligations left.
Self injury is among the most illegal and silliest routes to go. It would be far easier to get yourself disqualified with legal trouble. If you're going to be a crook, might as well be a healthy one.
In the end, most people survive their tours in Iraq, no matter how miserably. You can now join generations of soldiers who have bitter asked "Now why didn't I join the Air Force?"