How to stabilize this op-amp/MOSFET control system
You have a gain of 123 in the feedback loop and if an opamp were designed that could live with this amount of feedback gain then it would be a poor opamp indeed. The main suppliers design their opamps to have a small but significant margin of stability when operating in unity gain and you've blown that out of the water by adding over 40 dB of gain to the feedback loop.

Personally I don't see why any feedback gain is needed to make this a current source. The gain from U3 should be perfectly sufficient.