The load is connected from L1 to L2. The 208 volt Voltage vector is from L1 to L2. To produce 4800 Watts you must pass 23.1 Amps of current. However, Kirkofs law says that the current must pass from L1 to the neutral and then to L2. That is where the phase difference is.
You have two 120 volt windings each passing 23.1 amps but because of the phase displacement the resultant power is 4800 Watts instead of 120 x 23.1 x 2 = 5544 Watts.
If you split your load into two and used two 120 Volt transformers, you would have 120 Volts times 20 Amps on each leg.
To make it more interesting, The power is balanced on each phase even though the current is not.
However, current is what determines the voltage drops in the windings and the heating in the windings.
The basic rating of a transformer is the VA or KVA.
The voltage is fixed at the standard level that you choose to use.
The Maximum Amps are determined by the maximum allowable temperature rise of the windings.
Multiply Volts times Amps and you have Volt Amps.
Now you must put mechanical energy in in order to get electrical energy out. The Watts are determined by the usable Horse Power of the Engine.
80% power factor; This means that the manufacturer has decided, "Well, the alternator is 100 KVA, but the load will probably be at a power factor of 80% or worse, so I'll put a smaller engine on the set. I only need enought Horse Power to generate 80 KW."
You have mentioned a couple of times, low injector pressure. I've seen a lot of diesel gensets but I have yet to see one where the injector pressure is even monitored much less tied to a shut-down circuit. On many engines the injector pressure will rise when the governor calls for more power.
Let me try a scenario and tell me if it fits.
It's a cold and gloomy day. Everyone is staying inside and using more lights than usual. There is no sunshine and no wind. The chargers are working flat out to maintain the battery voltage, and the set is working fairly hard.
The oil is hot and thin. Now the pump starts. I expect from the loads that the generator slows down quite a bit when the pump comes on line. It may be that a 16 year old set, with hot oil, and slowed down by a heavy starting load, is tripping out on low lube oil pressure.
You may have a main bearing problem. A common symtom of badly worn main bearings is loss of oil pressure under load.
I remember years ago, a worn out diesel in a sawmill in the bush. The unit had a hydraulic governor. The engine and the governor were both so worn that if we lugged the set below about 1000 RPM, there wouldn't be enough oil pressure to operate the governor and the engine would quit.