How to null offset on op amp without affecting gain?
You need to use meg instead of m for the resistor value. You have specified a 0.007\$\Omega\$ resistor, which will tend to reduce the gain to 1. 

Your amplifier has a GBW product of 18MHz meaning it will only have an open-loop gain of about 500 at 40kHz, not the 14,000 you appear to be expecting. However it will have extremely high gain at DC so any offset will be amplified - so only a few uV will saturate the amplifier. 

You also need to bias the amplifier so the inputs and outputs are somewhere in the operating range- right now it will sit at the negative rail- you want it to be about Vdd/2. 

It's better to have a few AC-coupled stages with gain of ~100 or less rather than one stage which needs astronomical gain.