Opamp input offset voltage when saturation
I cannot limit the value of R2, in this case, how to avoid increasing
  this offset voltage?


The offset voltage is intrinsic to the opamp circuit, every opamp has an offset voltage. If you want to change the offset then the way to do that is with a different opamp. You will never find an op amp that can have both both inputs be the same value, you can find different op amps with lower offsets like auto zero op amps.

The offset voltage is not contributing to your saturation problem. It is offsetting the ground voltage on the negative terminal by -22uV, even with 5x gain, you'll have 220uV contribution on the output.

The saturation is happening because you are gaining 1V by 5x . 1V x 5 is 5V and that will saturate the op amp. So you can either reduce the gain, or increase the rails if you don't want saturation.