I was on my way to work and car started to run rough stumble and check engine light started to flash. Immediately turned around limped home about 3 miles. Changed plugs and swapped some old coils around. Still idles low and strong gas smell from exhaust. Any ideas need my car for work.
I believe you have a bad Engine Coolant Temperature Sensor (ECT in Ford nomenclature). The code P0116,the smell of gas, and the rough idle are all symptoms of a bad ECT. Its Ford's part number F5AF-12A648-AA. Get the OEM part. Its about $25. Be careful replacing it because your car has a plastic intake manifold that tends to break.
Based on the codes, I'd say race fever's spot on:
P0300 - Random/Multiple Cylinder Misfire Detected
P0116 - Engine Coolant Temperature (ECT) Circuit Range/Performance Problem
P0304 - Cylinder #4 Misfire Detected
P0174 - System Too Lean (Bank 2)
I believe what's happening is the coolant temperature sensor is giving no signal or a signal that's out of the normal range (P0116).
Under such circumstances, it wouldn't surprise me if the ECU assumes a default temperature which is an under-prediction when the temperature is warm (engine running rich, smell of fuel in the exhaust) and an over-prediction when the temperature is cold (resulting in the misfire codes).
I don't know if the ECT sensor is a common issue on this Mustang. Before you buy a new sensor, make sure that the sensor signal is getting picked up by the ECU using a scan tool.
If you obtain no signal or a constant temperature readout via a scan tool while the engine is warming up, this would indicate a loose connection or bad sensor.
Hope this helps.