[Radioroslyn]

I would make sure that any tube shields are in place. Try bypassing the the HV in the set. Can be done with a mfd or two  to gnd. If it still persists narrow down which stage is oscillating that shouldn't be. This can be done by touching the grid cap of the tube till you find the one that cause the oscillating to stop. If it turns out to be the IF amp you can try adding a bypass cap to the screen grid to gnd and or to the B+ side of the IF transformer. You can detune the IF transformer but there will be a sacrifice of gain.

Oh also be sure that your A and B voltages up where they need to be. Too low can cause stages to be unstable.

Terry