The way oiler uses a cam that the plunger ride up on and falls off about every 20 minutes when the spindle is enabled. If it is on the top of the cam, it has almost no room to move. But yes, it can be used manually by pulling up on the plunger.
The transformers terminals should be labeled. You need a schematic as to which wires feed it and which are the output. Typically these machines used "auto-transformers."They had only one winding with multiple taps.
The board you are showing is a BOSCH axis drive board. Not even BOSCH in Germany fixes them. EMI does not have a replacement.
A 460 volt machine means that the spindle motor and those transformers were all set up for 460 volts. The motor is easy to convert, so are the transformers. It is just a matter of moving wires.
If you use a phase converter, I would suggest you rewire the machine so the 2 good phases go to the transformers and control. The wild leg should only go to the spindle motor.
George
(Note: The opinions expressed in this post are my own and are not necessarily those of CNCzone and its management)