Is this the circuit we're talking about? My calculations and subsequent simulation yields diff=93nV (.000000093V).
I have never used strain gauges, but it seems pretty obvious that you will theoretically get no change in output voltage if all 4 resistors are active and facing the same direction. For most sensitivity, mount diagonally opposite resistors (R1 and R4, for instance) longitudinally, and, assuming there is little or no lateral strain, mount the other two nearby, oriented at 90 degrees to the longitudinal ones. This gives you temperature tracking.
Sorry about the homework comment. The 3 zillion digit resistor values made me think you were a student with no concept of significant digits.