There were several very different cars that used the Cutlass name. They included the Cutlass Supreme, a personal luxury car and then a midsize sedan, the Cutlass Calais, a compact car slightly larger than the Oldsmobile Firenza, the Cutlass Ciera, a midsize sedan popular in the 1980's, and the Cutlass Cruiser, a station wagon.
The first Cutlass was an experiment. Oldsmobile was trying to build a sports coupe back in the mid-1950's. Many years later a very similar car would hit production under the name F-85.
The first production Cutlass was a compact car for its time and was only made from 1961 to 1963. It was an A body with a V8 engine making 155 horsepower.
The Cutlass got bigger for the second generation from 1964 to 1967. A V6 engine was now standard, but V8 was an option, and there would be 3 of those engines sold during this generation.
The third generation Cutlass was the first where the car could truly be considered a muscle car. The top engine was now a true monster: a 7.4 liter 455 V8 making huge amounts of horsepower and torque.
By the fourth generation the Cutlass was getting boxy. Engine output was down, size was increased, and performance was down.
Some of these cars are now considered classics. The best place to buy a used Oldsmobile Cutlass is on eBay auctions. You can get some great deals on used and classic cars and there are also lots of parts on there.