Electronic hit detection
I think using modulated laser diodes and/or LEDs and photodetectors of some sort would be a much better idea.  Basically, turn it in to a game of laser tag.  It is much easier to detect an incident light beam than it would be to detect an impact, and you can transfer information about what sort of a weapon that it represents and who is firing it in the modulation.  You can get remote control receivers quite cheaply from some places and these will give you a demodulated digital output.  It would be simple to mount them in various places and monitor all of the outputs with a microcontroller to figure out where you got hit.  On the other end, all you need is an IR LED or IR laser diode that you modulate at the same frequency the detector is looking for.  If you gate the modulation with a serial signal (i.e. UART) then you can pass along information about what type of weapon it represents and who fired it and decode this at the receive end.  

If you really want to detect impacts, a piezoelectric solution may be the way to go.  The hard part will be making a solution that is insensitive to orientation and vibration while also being able to cover the entire external skin of the vehicle.  There will likely be a significant tradeoff between false negatives and false positives and it could be very difficult to make it robust enough for your purposes.