O2 Sensors just provide feedback to the ECM about the engine running rich or lean. I don't think a bad or dirty O2 sensor would cause a surge during acceleration, rather just run more rich or lean than it should. Your best bet would be to pull the codes and see what the ECM think's is going on. Jrichker has a good post on how to pull the codes using just a jumper wire or paperclip.
Dump the codes and see what the computer says is wrong…Codes may be present in the computer even if the Check Engine light isn’t on.
Here's the link to dump the computer codes with only a jumper wire or paper clip and the check engine light, or test light or voltmeter. I’ve used it for years, and it works great. You watch the flashing test lamp or Check Engine Light and count the flashes.
IF your car is an 86-88 stang, you'll have to use the test lamp or voltmeter method. There is no functional check engine light on the 86-88's except possibly the Cali Mass Air cars.
89 through 95 cars have a working Check Engine light. Watch it instead of a test lamp.
Codes have different answers if the engine is running from the answers that it has when the engine isn't running. It helps a lot to know if you had the engine running when you ran the test.
Trouble codes are either 2 digit or 3 digit, there are no cars that use both 2 digit codes and 3 digit codes.
For those who are intimidated by all the wires & connections, see http://www.actron.com/product_detail.php?pid=16153 for what a typical hand scanner looks like. Normal retail price is about $30 or so at AutoZone or Wal-Mart.
What year of stang do you have? If it's a 94-95, there have been instances reported where a bad O2 signal caused surging. It seems to be much less likely on a fox (the foxes run rich in FMEM and 5N's run lean).