well if it was running well before the petronix III that is one thing.
oil on the threads, means valve stem seals need to be looked at. Big job as far as work involved. I did mine this summer took a full day and i did not enjoy it even with help from the engine builder. that is if the plugs are fowled with oil
if the plugs are fouled with fuel, that means weak spark or incorrect timing.
I do not know exactly what you are running on your engine but i will give you this direction to look into.
If you changed to the petronix III and used the petronix Coil and changed the ignition wires. what ignition wires did you change to?
if you changed the ignition wires to the recommended petronix 8mm spiral core or what they claim are shielded wires, take them off the car and throw them out.
Get a regular Ford Carbon filament standard set of V8 ignition wires. start the car and let it run to burn off the plug fouling, then check the timing you will see it changed. reset the timing to what you want and go for a spin.
I went through this i had some 8 and 9mm MSD wires and the engine ran like pure garbage until i advanced the timing to the moon. miss on acceleration, ran rough,etc... changed out the aftermarket ignition wires for old school regular ignition wires. instantly the engine ran almost perfect.
before you start to freak out about the plugs being fowled which is more a symptom of a spark problem, look into the ignition wires themselves then the carburetor.
I personally hate the petronix III. the I or II work better with our cars if you have the stock tachometer.
i hate high powered coils also they cause all kinds of radio interference issues.
before you go nuts, first see what ignition wires you have. anything other then stock, throw them out, and grab a set of regular ignition wires no frills no special insulation, no special silicon wrappers. just good old carbon filaments, install them and see what happens i'm sure there will be tuning required but you want to see the effect on your car.