How to estimate force caused by a strain in a material from a strain guage?
Gauge Factor is the first element you're looking for.  

As described in that link to Wikipedia, the Gauge Factor of a Strain Gauge is the ratio of relative change in electrical resistance \$ R \$ , to the mechanical strain ε, and is defined as:  

\$GF = \frac{\Delta R / R}{\Delta L / L} = \frac{\Delta R / R}ε = 1 + 2v + \frac{\Delta \rho / \rho}ε \$
where  


ε = strain = \$ \Delta L / L_0 \$


\$ \Delta L \$ = absolute change in length
\$ L_0 \$ = original length

ν = Poisson's ratio
\$ \rho \$ = resistivity
\$ \Delta R \$ = change in strain gauge resistance due to axial and lateral strain
\$ R \$ = unstrained resistance of strain gauge


But knowing the gauge factor of your strain gauge(s) is only part of what you need to calculate the force exerted on a load cell.
The mechanical construction of the load cell determines the relationship between the \$ \Delta L \$ of the strain gauge(s) to the amount of force applied to the load cell.
It's been a while since I last worked with mechanical engineers who understood and explained those details to me, but this factor obviously depends on the material the load cell is constructed from and the dimensions &amp; geometry of the construction.