How to convert between G and mV/g of sensitivity?
You have been reading literature that uses the word 'sensitivity' carelessly to mean two slightly different things. The usual sense is 'what is the smallest change in g that can be detected'. However many people will also say that a higher gain accelerometer is 'more sensitive'.

Unfortunately, while sensitivity and mV/g are related, you need other values specified to relate them.

The mV/g is simply the gain of the accelerometer, the ratio of output voltage to input acceleration. That's quite easy to measure. If the acceleromter is sensitive to less than 1g, you measure the output, turn it over, and measure again. That's the change of output you get for a 2g change in input signal.

The sensitivity depends on the noise of the total system, including the accelerometer, any analogue signal processing, the ADC, and any digital signal processing, and crucially, how you define sensitivity. Usually, one of these components will dominate the noise level. If it's the ADC resolution, then a simple scaling of the ADC LSB with the gain will give you a g figure. However, the ADC might be more noisy than one LSB, or you might do some post-processing to reduce the noise below one LSB (it can be done, for some ADCs). 

So you need to know the noise. An active accelerometer will generate some of its own noise. Unless that's specified in the data sheet, you won't know that until you buy it. It's likely that you'll be able to build a lower noise signal AQ system and the accelerometer noise will be the limiting factor. The noise from a passive strain gauge should be possible to estimate if you're told the resistance in the data sheet, and your amplifier will probably be the limiting factor there.