+1 on Midridge2's comments. The oil issue is likely to be a red herring unrelated to the running problem. However, before discounting it, do check the oil level again and make sure it is not overly full.
You said the car is relatively new to you. Don't assume the previous owner kept it in top tune. Assume that the car needs a basic tune up. Do you have a manual for the car? If not, buy one. While you can get a lot of the information online, there is a lot to be said for being able to read through the steps multiple times while looking at exploded diagrams and pictures.
That said, always start with the ignition system and do not jump right into tweaking the carb.
Adjust the valves (cold).
Inspect the distributor cap, rotor, spark plug wires, and plugs. Replaced any cracked or carbon tracked components. When removing plug wires check them ONE AT A TIME so you do not put them back in the wrong order or location.
From the factory your car will have points in the distributor. Clean, dress, re-install and gap the points to the correct clearance. Make sure the cam that opens and closes the points is lubricated (45D distributors have a felt wick that must be oiled, earlier 25D distributors require a smear of grease on the cam lobes that open the points). Replace the condenser... just because.
DO NOT assume this is the coil. People love to say they had a coil fail and replacing it made everything better. What they often admit later is that they also replaced the points, condenser, cap, rotor... at the same time... so you don't know which component failed.
Regardless, go through these ignition areas first. However, you CAN and should check the carb dashpot oil as OfMini&Men suggested. Unscrew the cap on top of the carb and pull out the brass rod assembly. Looking down in the carb you will see a center metal tube. Pour 20W oil into that inner tube until the oil is about 1/4" below the top of the tube. You do not need to go buy a quart of 20W oil for this tiny bit. If you are in a hurry, the 20W50 you are running in the engine will be OK. If you want to run 20W, go to Home Depot or Lowes and get a small bottle of 3-in-1 oil (the blue bottle is 20W, the red bottle is 30W). The 3-in-1 bottle is small enough to carry in the car at all times should you need dashpot oil in the future.
Anyway, start by going through an ignition tune up. If you are unsure how to dress and gap the points in the distributor, post back and we'll walk you through it.