Overdrive on or off?

My answer was going to be, "depends", but it looks like it's been answered pretty well.

Is your button labeled "O/D Off" or "Tow/Haul"?

If you have an "O/D Off" button, it's an older chassis with the four speed transmission and the button simply locks out the fourth (overdrive) gear. This can be useful when driving through areas of rolling hills, etc. You can also make it kick out of overdrive by pushing the accelerator down far enough to make it downshift.

If it's labeled "Tow/Haul," you have a newer five or six speed transmission, and the button does not disable overdrive. It instead alters the shift logic some to optimize it for heavier loads--tending to stay in lower gears longer, downshift for engine braking, and avoiding unlocking the torque converter so as to keep the transmission temperatures cooler, perhaps among other things. Since a class C motorhome is a large load for the chassis, it's perfectly reasonable to leave tow/haul engaged all the time. It's especially helpful in hilly or mountainous areas.

a mechanic told me if it has over drive factory installed it is OK to use it when on the open road. that's why it is there. like the above post states, if the tranny is searching for gears, it is time to turn it off and down shift. when the road is level or going down a hill, turn it back on.

I would be in overdrive unless it starts to downshift frequently. What is frequently? Make it 15 minutes or less.