When the check engine light came on my 2002 Lincoln LS the engine began to run rough and there was a strong odor (maybe catalytic conv?). Only 77k miles. It is still running very rough.

A bad converter will cause a loss of power not really a rough engine problem. Often rpms will rise and mph will fall.
First Scan for codes. A misfire is possible, a tune up is suggested if you haven't done one.
1. look for vacuum leaks or maybe a wrong PCV valve. If using a scan tool to look at the Barometric Pressure (BARO) PID to see if the Mass Air Flow (MAF) Sensor is in calibration. 2. Look at the Delta Pressure Feedback (DPFE) Sensor. The original DPFE was metal and had a very high failure rate. It can fail and not set any codes. Identify the type of sensor 9 Metal or plastic) then look at the output voltage. Metal normally reads 0.4v to 0.65v, the plastic sensor is normally about 1.0v. Replace the DPFE as needed and see what happens.