Has anyone answered your question how to wire the contactor in the pic? What you have is a 3 phase contactor. L1,L2,L3 = 3 phase. It is possible this contactor was used on 3 phase 440v making the coil 440v. Is there any info about the coil?
This is only a guess, need to confirm with an ohmmeter. The red wire is a part of the control circuit. One control leg from the pressure switch will feed in on the long red wire, goes to NC, normally closed contact, which will open if the bottom section measures too much current. The power then is sent to T4 via the other short red wire. My guess is T4 is one side of the control coil. Now use your ohmmeter and try to determine which screw is the other side of the control coil, I would try T3. If it is T3, that will be the other wire going to the pressure switch.
If there is no info about coil voltage, make up a cord and apply 220v to the coil. Going to say that if you get it right, the blue section will pull inward when the coil is energized.
Then all you need to do is apply 220v to L2 & L3 and wire T2 & T3 to motor.
Now, don't forget to put all this inside an approved electrical box or the NEC COPS will give you a ticket and push you over a cliff.
If you can't get the contactor to work and you find out how much one is going to cost you may want to double up the switch like I said above. Then put the all air compressor inside a metal container, turning it into an appliance. Then make and break one side of the 220v. The metal container will make it safer, NEC approved appliance. You may want to put a grounding rod on the metal box too. Wouldn't want to upset the NEC cops.
By the way, a code is not the same as a law, except here. You can be arrested if you break a law. Never seen anyone get arrested for breaking an NEC code. If you could, I would be serving a life sentence.