What sets the resolution of an analog resistive sensor?
If we define resolution of an analog measurement as the smallest change which can be detected, there are some limiting factors. In this case, we're talking about change in strain, not the resulting change in resistance, though obviously they are related. 

For the sensor itself, there are factors such as temperature coefficent, hysteresis, 1/f noise (drift) and Johnson-Nyquist (white) noise. The white noise effect can be mitigated by reducing the bandwidth, but then 1/f noise becomes more important, so even if you have no constraint on the time to take a measurement you can't reduce the noise effect without limit.  

To the extent you can know the temperature (and to the extent that it's consistent over the element) and you know the strain history you may be able to compensate partially for some of those factors.