2002 Mustang SRS with 208,000 miles on it.

This is definitely not an oxygen sensor problem. The Engine Computer just fine tunes the fuel / air mixture based on its readings. The first thing you have to do is determine if this is being caused by an engine misfire or a drive line vibration. Worn or tight universal joints can cause a shudder, especially under load or during acceleration. A misfire can cause the same thing. For that, start with the basics, spark plugs, wires, and ignition coil. If those don't solve a misfire, there's most likely a reason you got a good deal.