If you can't move the cable it may be rusty, most are the spring type that can be lubed by spraying the outside. You can take the cable end off the at the transmission and work it in and out to check the cable.
The cable operates a lever on the tail shaft section that will allow the overdrive to work. Its a mechanical lock out. On my transmission when you shift to reverse a internal rod locks out the overdrive, I've had it on the work bench testing the operation before the install. The only time the cable can't be moved is in reverse.
Remove the O/D shift lever from the tailshaft. Soak the entire cable assembly in PB Blaster or some other penetrating lubricant. Allow the cable to soak for several hours. If it comes free, continue to move the handle in and out to further free up the cable. Re attach the O/D shift lever and test again. If everything works smoothly you are ready to test the O/D as noted in the previous posts. If you fail to free the cable after a couple of days soaking, replace the whole cable assembly. Chris at 1-405-259-922 can provide the part if you need it. Price is $49.95 and is shown under 49-53. parts/transmission/page 4.
Ok, I went ahead and took the cable off and set the overdrive as if the handle was in. I tried to pull the car out of the garage and problem number one. It will not go into gear. So after pushing it out to the street, I took it for a ride down a long road. So, its definitely working. I noticed it in third doing about 50 and had that free wheel when I let off the gas instead of what felt like a standard trans wound up to high. So I presume that the lockout switch is an issue but if I can get the handle to work then I could manually make it work.