Cutlass has stoped reversing

One possible cause is a stuck torque converter solenoid. The car acts like you pop the clutch on a manual shift model.
Does it happen in reverse too, or just drive ? And can you raise the idle speed and prevent it from stalling ?

have someone shift the the trans while you look and see if shifter cable or linkage come loose or not working period look and see if there is a leak or puddle on ground check fluid level not knowing where you are from and it being older car i have had one break from it being frozen

This is a symptom of a failed transmission, ie no reverse gear engagement. You will need to rebuild the transmission.

That is your call

Nice car,I wouldn't junk it,only to pay
$45,000 to replace it.

Spend the $2,000 for the reman trans

Not for Reverse. The transmission will need replaced or rebuilt.

Sounds crazy but, check for bad injector[s] Wadski

Sorry, there are no electronic controls for reverse on the 125 trans. It will need rebuilt or replaced.

Overdrive has two important factors involving when and if it turns on besides being in the proper gear shift position. One is tthe car has to FIRST reach operating temps before it will engage the TCC ( torque converter clutch ). That could involve a faulty thermostat, or short distance drives, Second important factor WILL DISENGAGE WHEN STEPPING ON THE BRAKE PEDAL. A brake switch could be misadjusted , and without you stepping on the brake, the computer thinks you are and wont engage TCC. Hope this helps.

When is the last time she had a tune up?
I would start there. Plugs, Wires, Distributor Cap and Rotor. Hope this helps you and thank you for using FixYa!