Here is a circuit that I suggest for your strain gauge amplifier – sooner that I thought!
The amplifier is the classic three-chip design using an LTC1053CN. This is a quad chopper-stabilized amplifier that has offset voltages better than 2microvolts. IC2 and IC3 together amplify the differential inputs from the cell. The gain is determined from A = (R1+R2)/R3. With a 10V supply the cell will give a maximum swing of 0 to 20mV. You need a swing of 0 to 5V so the gain needs to be 250. With the values given, A = 2 x 15K/120 = 250. Those are followed by IC3 operating at unity gain that converts the differential voltages to a single output suitable for your micro.
Even using 1% resistors, calibration will be required so, rather than fitting a trimmer as part of R3, I thought it easier to change the cell output as necessary by modifying its 10V supply voltage. So the cell (and amps) are run from an adjustable voltage regulator.
I suggest using an LM117 regulator IC. It has an adjustable output voltage and a 1.75V dropout voltage (the difference between your battery voltage and the maximum voltage you can get from the IC). So if you are using your car battery with the engine running, its voltage will be nearer 13V and you will be able to get up to 11.25V from the IC. It provides a very stable voltage, independent of load. Its output voltage is set by the potential divider R4/R5/R6. This provides a feedback voltage of 1.25V to the ADJ pin, so depending on the setting of R4 it will give between 9.75V and 11V at the output. R4 is set nominally to give +10V and adjusted from there to calibrate the cell.
Here are the datasheets for your further information.
http://www.datasheetcatalog.org/datashe ... 009063.PDF (LM117 Regulator)
http://www.datasheetcatalog.org/datashe ... zcpl7y.pdf (LTC1053CN) (CN= in small package)
Just a few points to note. Use ¼W metal film 1% resistors. Fit R1, R2, and R3 as close to their respective pins as possible. Keep leads as short as possible. Use a high-grade pot for R4. Fit the capacitors either side of the LM117 as close to the pins as possible, and be sure to use a tantalum for the 1µF. If the op-amp is more than a couple of inches from the 1µF tantalum, then fit a 100nF across the supply pins to the op-amp - as close as possible.
And finally, best of luck.