the problem is not with the strain gauges but how to define that the adc is from 0V to 5V but having 2.5V as reference so it can go below and above.
If you feed a 2.5V input to VRef, the ADC will report values from 0 to 1023, still, with measured values above 5.0 being clamped. This is not what you want.
Typically, the strain guage output would be fed to an op-amp with an offset of 2.5V, so that the range of values being measured still fell between 0 and 5V, with 2.5V being the relaxed condition, and lower voltages representing compression and higher values representing tension (or the other way around).