My 56 has three speed with overdrive, a great system. I keep looking for a 59 Sport coupe with V8 and overdrive in Hemmings as well as other publications but they seem to be absent. I have expanded my search to 58's and 60's but nothing. What happened to these cars? Everything available either has PG or 4 speed.

Overdrive was most popular from 1955-1957....by 1959 they were few and far between when new.The exception probably would be cars sold in the great plains states.
I will agree. my 1957 with O.D. was the perfect road and city combination.

Many of the automatics over the relatively recent years have or had overdrive (OD).

"Overdrive" merely means there are more rpms coming out of the transmission assembly (TA) than going in. "Drive" means straight through the TA with the same revolutions coming out as going in. Nowadays, you can ask you average new car salesman about what OD means and he or she won't have a clue.

As to the old mechanical overdrives, there was not much of a gain seeings how you got a lower ration rear end with one. Example, a 50 Ford with just without OD would run about the same wide open (as fast) as one equipped with OD and it engaged. Not enough HP to make much of a difference. (Depending on direction and speed of the wind, of course.) The OD did well at cruise speeds of 45-55, or so. There may have been a slight increase in gas milage vs just drive at those speeds. Especially with a good tail wind. The forgoing is just my experience and opinion.

The fastest drag car in town in 1955-56 was my buddies black and white 55 Chevrolet conv. My 56 Chevrolet conv. with automatic only ate its dust. His 55 had manual transmission with OD and power pack (four barrel and duel exhaust). When, dragging, he would deactivate the OD. Thing would scat! That was mainly owing to the lower ration rear end that came with the OD and the power pack.

This was an interesting question. Glad you asked it. It brought back many memories.
Charlie