Current controller: how to dampen resonance to increase bandwidth?
The opamp is oscillating...

This is due to the feedback inductor current, which has 90° phase lag relative to output voltage. Since the opamp's output already has about 90° phase lag relative to input voltage, you get 180° lag and it oscillates.

"I have no idea what I'm doing" method:

The 20R resistor on the output is part of the load?

Remove the top series RC (can't see the part names on your schematic) and add a cap from the output of the opamp to the negative input, perhaps 100pF. Adjust its value until the frequency response looks good, you should get rid of the peak.

Engineering method:

Learn about bode's stability criterion. (VF)

Now, plot the open loop gain by breaking the loop and inserting a source inside:

http://www.linear.com/solutions/4449

Then do the above capacitor trick...

Then close the loop, it should work.