You're confusing me. Did you purchase the compressor and Phase converter as a unit together?? I assume the converter is of the appropriate voltage for compressor. (there are different 3 phase system voltages) Be sure the converter output voltage matches the needs of the motor on the compressor.
I assume you need a certain voltage to that converter. What does it need 120V, or 240V to operate. Once that is determined feed the converter with the appropriate voltage and amperage (circuit) for it and the compressor to operate.
Then you mention a 4 prong plug for the compressor and use that outlet. WHAT OUTLET? Is there an outlet on the phase converter to plug the compressor into? If that is the case the outlet should have a NEMA number imprinted on the front indicating amperage / voltage and NEMA configuration 15-xx or possibly L15-xx (the "L" indicating it's a twistlock receptacle). Once you install the appropriate plug put into the receptacle, energize the circuit and turn on the compressor. BE AWARE that the motor could possibly run backwards. If this happens shut everything off, remove the plug from the receptacle and change any TWO of the THREE power leads to a different terminal on the plug. Put it back together and try it again. It should be running in the correct direction now.
I stress though be sure the Voltage on the converter matches the Voltage on that motor.
You may want to hire an electrician to take a look at it. I mean if you saved that much money purchasing it, there must be something in the kitty to have it hooked up properly.
I did not comment on the phrase "Or do I have to use 3 prong 240 Volt without the 120 line." I have no idea what that is supposed to be referring to.