AGC with multiple op-amps
You cannot perform this function in real time with an analog AGC, although you can get close with a fast enough processor.  The problem with traditional AGC is that it relies on previous information to set the gain, and if I understand your problem you are trying to measure impacts that may occur in different positions relative to the four mikes.  The analog inputs previous to the impacts are not indicators of the impact amplitude and therefore can't be used to determine gain.

You will have to "look into the future" by sampling data and then analyzing a set of samples that contains your impact with some surrounding samples.  Then you can then normalize the response and compare the timing on the processors.  Do this repetitively with overlapping sample sets and you can get by with only a small lag in your output from the impact.  DSP chips are ideal for this type of work.