When driving down the road should the transmission be in drive or overdrive?

2001 chevy.. what Model so FIXYA Folks can help.

The overdrive will only come into use when the transmission module reads the correct revs/ road speed ratio. Switch if off for heavy city traffic driving to improve economy when it moves up and down all the time. No it will not harm the transmission otherwise.

Sounds like you have a problem in the Overdrive sensor or the lockup in the converter. You should see if a scanner will identify this problem. Ask at the autoparts store about "What they show for an Overdrive switch or Servo?". Autozone, Advance, and Oreillys do free scans.

Check your transmission fluid as the trans works hard in top gear with pressure directly driving the tallest gear in the trans. Low fluid levels could be causing the converter to kick out of Lockup.

overdrive is just what it sounds like-the transmission turns slower than the engine, allowing more speed with less fuel. It is only applicable in higher speed, low load situations like open road driving, but most modern cars with overdrive will allow engagement at speeds as low as 35 MPH to save fuel. To a point, overdrive is effective for some city driving, but if you constantly do stop and go driving, in city enviornments at speeds under 40, it is best for the engine (and performance) to 'lock out' overdrive.

There is an electrical problem with the transmission. Stuck actuator or something. Get it checked, might be a $200-300 fix, that would cause a transmission failure down the road. It might even be the overdrive switch on the shifter.

try servicing the trany and putting in some lucas transmission treatment. sounds like the tcc is sticking and needs some lucas to clean it and lube it up.

This is an improper reading from the input speed sensor.

High to low /low to high ratio, you will need to be stopped and the transmission in neutral for this to be changed.
The 2wd - Auto - Lock switch can be switched at any time, as it operates an electromagnetic clutch - 2wd is rear wheels driving only - Auto - is to automatically engage 4wd when wheel slippage is detected (this also happens when turning at intersections, due to the inside wheels having a shorter path to the outside wheels, and can give a binding effect on sealed roads (I don't drive with it in auto on sealed roads) auto is excellent if you get, or expect wheel spin from an intersection when wet, just flick it on before or when you have wheel spin, also on gravel roads, having it on auto will greatly reduce the sliding of the back end, and make the car noticeably more stable.
Lock - this locks the differential, which further reduces wheel spin, when in mud / snow, but this will also make the car not want to turn corners, due to it resisting the different distances traveled by the inside and outside wheels.
A/T switch - this actually has 3 positions, and changes the shifting points of the automatic transmission - the middle is normal - Hold is to hold the gear longer, to improve fuel economy, and not change down (kick down) as quickly - Power has the opposite effect, it makes the transmission change down sooner under acceleration.
Also the O/D (overdrive) button on the side of the Tee shift lever, is to engage / disengage overdrive (5th gear) - never do heavy towing in overdrive, this will cook the transmission and overheat the engine (due to the radiator being used as a heat exchanger for the transmission fluid.
Another little quirk - if the transmission light starts flashing every 40 to 50 km, this can indicate that the wheels are different diameters (a flat tyre, or tyres have been swapped around and the spare is more or less worn than the other tyres), the computer will pickup that the wheels are turning at different speeds.
When cold, it is normal for the transmission to stay in 3rd (2-3 minutes of driving), until it has warmed up, and then stay in 4th for a few more km's (5-6 minutes), before it has warmed up enough to change into 5th (overdrive).

Most likely causes is the OD shift solenoid or less likely the VSS

OK, here is an update - The torque booster pump broke, so I had transmission rebuilt at Benchmark. So far a year and 20K miles later we have no problems.