Is this a good/acceptable design?
Hard to tell as it is very application specific. Your design, inspite of the "differential input" designation, seems to be single-ended - utilizing a true differential (bridged) configuration would be helpful.
Where is there room for improvement.
Assuming that the strain gauge signal comes off a bridge configuration, I would do a few things:
1) do away with the diodes and utilize a regulator to create a virtual ground. Something like a 7805 would work here.
2) balance out the non-inverting input: use a 1k//10k pair to ground to minimize out dc errors caused by input bias current;
3) lift the non-inverting input off the ground;
4) unless you are absolutely sure of the load, put a small serial resistor on the output.
5) I would pick a jfet opamp (a single) so you can adjust dc output.