If you haven't already, go to your school police officer or local police station and report the theft. You have to get his name inside the system because it isn't likely this is the first time he stole something and it certainly isn't the last. Don't be lazy about this, you have to do this. I don't know how effective your area's police force is but you might have to badger them a bit to get them to take action. You should also talk to your teachers for some advice. This might be as far as you can take it legally, once again talk to your local police officer to details. If you know your friend has abused drugs you should also bring this up as well. Also, gather the serial numbers for the PSP and your headphones, the police will need them. Also, go to your police department's website and see if they have a theft form you can print out and fill out. If they're under 18 they might get just community service. If they're over 18 they can become a felon which won't look good for background checks when he tries to get a job. The circumstances might change if the items were purchased under a parent's name. Perhaps you can use that to your advantage.
Now it is time to engage things more personally. Like I said before this probably isn't the first time he has stolen. There is someone at your school that also has had their stuff stolen by this guy, try using facebook to find them and get them to file a report to the police as well, this will help a lot if you can't get solid proof that it was him. If you have a facebook you can try setting your status to something like "Anyone have their stuff stolen by ____? If so contact me so we can report it to the police together." I doubt that your friend has a good home life but you can try talking to their guardian(s) anyway. Have your friends check out local pawn shops to see if they have been sold there. Also spread out and scan some of the local hot spot hangouts to see if anyone is rocking your headphones. If you spot them don't say immediately that they're probably stolen, sweet talk them a bit and say that they look cool. Ask them where and when they got them.
You said you keep getting backstabbed. Sit down and spend some time analyzing why this is so. Do you give your trust out too easily? Do you make friends with the wrong people? Even backstabbers have people they trust, then, why don't they trust you? Perhaps your end of the friendship doesn't bring anything they want to the table and that is why they part with it so easily. This means you either are a poor judge of character or you don't know yourself well enough. Both of these can be fixed but they take time, however, your real friends will be happy to help.