There are several other names for your 120/240V 3 phase 4 wire distribution system, they include: wild-leg, high-leg, and christmas tree. The most common construction is two single phase transfomers connected in an open-delta configuration.
One transformer is siginificantly larger than the other. The large unit is sized to provide 3 phase and 1 phase loads, and has a center tap, so you can get 120/240 single phase from it. The other, smaller, unit is there to provide 3phse loads only.
Your strange voltages come from the delta configuration. On the utility side of the meter these are A-B 240V, B-C 240V, C-A, 240V, A-N 120V, B-N 120V, and C-N 208V. On the customer side of the meter (the area covered by the NEC) the B and C phases are swapped, so B-N is 208V and A-N-C is 120/240V single phase.
Never connect single phase loads to the high-leg.
Always use 240V breakers (not the standard 120/240V ones) when connecting any 2 pole loads to the high leg.
My personal preference is to install (1) 3-phase panel (without a neutral bar) for the 240V loads and a seperate 1-phase panel for the 120/240V loads. This prevents a lot confusion when adding breakers, because you don't have to skip the high-leg bus bars.
