Also, there are plenty of ways to test everything involved. A simple multimeter can check the 2 ohm values of the primary. One of those transistor tester gadgets ($20) can test the inductance of all of the coils.
You can't really test the phase relationship with a cheap gadget, but you can do that with one or two AC "wall wart" power packs. Any voltage will do, something like 5VAC or 9VAC or 12VAC. You can also open up any unregulated DC "wall wart" and just remove/bypass the bridge rectifier (sometimes it's just 4 diodes on the PCB) and the capacitor.
Then, just put the voltage into whatever wire pair you want. You can hook it up to the secondary, and then test both primary components and see if the two primary coils are in-phase or out-of-phase. You could also connect them to the primary, and test the secondary and/or the other primary.
I am not yet an expert on transformers, but I suspect this transformer was not intended to be run with the primary coils paralleled. It appears to be setup for either 120 or 240V operation.
In any case, you can also use the combination of the above tests to get corroborated data. You can use the multimeter to test the ohms ratings, and use the transistor tester to get the inductance ratings. You can estimate the turns ratio by this (with a simple calculation)
You can then use a wall wart to power one of the coils, and then estimate the turns ratio by this as well.
If the two ratings agree, then all you need to learn is the phase relationship.