In opamp feedback circuits, it's all about the current flowing in the feedback network, which must balance the current flowing from the input. Clearly, the transistors are intended to modify how the feedback network passes current, so the question is to figure out how they do that.
The basic feedback is provided by the string of resistors in the middle, which pass current according to the voltage difference divided by the total resistance. As long as the voltage across either of the 22K resistors is less than about 0.6V, neither transistor will turn on, and you have a basic inverting amplifier with a gain of about -10.
However, if the output voltage exceeds about +14V (note that the "" input of the opamp is held at "virtual ground"), the lower transistor will start to turn on. This will pass extra current through the feedback network, reducing the gain of the amplifier overall. In terms of the application, this provides a "soft clipping" or "limiting" function. The other transistor conducts when the output tries to exceed -14V, making the operation symmetrical.
Note that the diodes are required in order to prevent current from flowing in the "wrong" direction through the 22K resistor and the B-C junction of the corresponding transistor.