Dynamometers

If you know the power transmitted from the wheels to the dynamometer and the RPMs of the wheels you can calculate the torque at the wheels by a simple formula:

Torque = (Power / RPM) * ( 30 / pi)

where Torque is in Nm (Newton meters) at the wheel, power is in W (Watts) and RPM is the RPM of the wheel, not the engine. (None of them arcane Imperial units). Size of the wheels does not factor in.

Knowing the torque at the wheel you can calculate back to torque at the crank using gear ratios and final ratios as you suggested (ignoring for the moment power losses through the tranny etc., it will get you close)

I know how to convert torque to power. In a dyno, though, Torque is what is measured, not power... then power is calculated.

My question is, how do the Torque measurements vary when using different gears. Will the dyno readings change (as I mentioned) from gear 1 to 2 to 3 etc.?

Yes, the actual torque on the wheels varies with gear ratio. Ideally you use the highest gear for a chassis dyno test so that you maximize the load on the engine and to minimize the rotational inertia effects of the drivetrain as the dyno test is done. At least with a rolling drum type dyno, where you are measuring the rate of acceleration of the heavy drum to determine the instantanous torque applied.