Okay, in every scenario, the postal truck has no importance whatsoever. In fact, the police might stop and check out the reason he's equipped himself with lights and a blaring siren.
The fire engine and the ambulance have equal priority, because either could conceivably be trying to save someone in a medical emergency. That seems to take priority.
The police car is the better equipped for making up for lost time. It's small, and won't be carrying a patient. They should let the ambulance and fire engine through, then jet forward across the intersection ~ unless, of course, arresting the driver of the postal truck is more important, then they should just stop in the middle and attempt to cut him off.
So the priority would be:
Ambulance
Fire Engine
Police Car
Postal Truck
However, having given it the thought you suggested, I would say the answer is: which ever two, from the police car, ambulance, and fire engine, are going parallel to each other should go first, the the other should go second. That would be the best answer.
The postal truck has nothing to do with it.