With circuits like your example schematic, with a single input to the opamp - and the opamp + input to a fixed voltage or ground, the gain at each stage is proportional to the ratio of the input resistor to the feedback resistor.
eg. The left hand part of the circuit has 10K (R6) input and 470K (R7) feedback; 470 / 10 = 47. The output will be 47 times the input (and inverted).
The right hand half has 20K input (R3) and 470K feedback (R4) so the gain is 470 / 20 = 23.5 times the input, and again inverted.
Total gain 47 x 23.5 = 1104.5
That assumes the signal levels are always in the range the opamp can handle and give the correct output for.
Unless that is the exact circuit for that PCB, there is no way of knowing what gain it gives, other than makers data or trial and error.
If it is the circuit, R5 is presumably the external connection to the gauge.
A high quality strain gauge unit normally has four elements (R2, R5, R8 and R9 in that diagram) with two opposite diagonals under compression and the other two diagonals under tension, when the part being monitored is put under load.
That's a "full bridge" configuration.
More info:
Learn more about fundamentals abour measuring Strain with Strain Gages.