how do I stabilize opamp amplifier oscillation
A bare bones OP-AMP is "close-to-unstable" in a lot of circumstances (even in very simple circuits). There is a parameter called phase margin and this informs the reader that at unity gain, the inverting input is significantly close to being non-inverting - phase margin tells you how close the inverting input has become a non-inverting input.

For instance, a typical op-amp might have a phase margin of 40 degrees. This means that instead of the inverting input producing a 180 degrees shift (i.e. true inversion) it is more like 40 degrees.

This of course will be at a high frequency where the op-amp's characteristic has dropped to unity gain i.e. far above where you would consider using it normally. But it's still there in any op-amp circuit you might design.

If you add transistor amplification (say 20dB) after the op-amp output (and before the feedback), you will now have a phase margin that is 40 degrees at a gain of 20dB and, if you determined what the phase margin is at a higher frequency (one where the extra 20dB is eroded to zero dB) you'll almost certainly find that the phase margin passes thru zero degrees and therefore you have created an oscillator!!

Here is a similar question/answer

EDIT - I've added a picture of the open-loop gain and phase of a medium speed op-amp to consider: -



This graph is the basic operation of the op-amp in question (AD8605) and is irrespective of how you apply feedback and how much you apply. The only point is that the red line (gain) will rise maybe 10dB when you put transistors within the feedback loop.

With the red line rising by 10dB, the unity gain crossing point is around 30MHz - what is the new phase margin - it's probably about -40 degrees i.e. well past the point of stability. Look at the graph - with sufficient gain added inside the feedback loop, this device (AD8605) will oscillate at about 25MHz.

Lower the gains in your transistor circuits is my advise.