Yes, a fouled plug and/or wire can cause the car to "studder and shake" violently, through idling and acceleration. As long as your car can still drive (albeit poorly), that is usually a bad wire or plug.

Usually having too much oil, or a stuck open valve (as I was mentioning earlier), would cause the car to not even start or would let the car start but then stall and die within seconds of initial startup, so I don't think your problem is that severe.

Try the plugs/wires tomorrow and let us know the outcome.