understanding oscillation in op amp circuit
Why don't these oscillations take over the signal? If they are created
  from positive feedback, shouldn't they keep growing?


The main factor that springs to mind here is slew rate limiting. 

At some position in the bode plot, the gain is above unity and the phase is at 180 degrees and simplistically, a sine wave would be expected to grow until it swamps everything. But it can't attain an amplitude that is beyond the slew rate limitations of the op-amp. This is why you sometimes see a small amplitude sine wave riding on the back of your signal.

There can be other mechanisms as well but I expect slew rate limiting to be one of the more significant factors.