My Golf 4 having rough idle. Black smoke coming out of exhaust instead of steam. I've changed engine oil, filter elements, spark plugs, cleaned throttle, scan detected O2 sensor and engine spe

What color is the smoke? White smoke is oil burning, black is fuel. There are a dozen things that could cause the symptoms you describe. Faulty fuel pump, dirty injectors, ignition system fault, cracked cylinder head, bad fuel, faulty engine sensor (MAP, OXY) etc. Really need to find a mechanic who can look at it in person.

Smoke is not a good sign. Running rough is not a good sign. Oil light not a good sign. You could have a combination of bad things, most likely expensive. Suggest professional help. Smoke can be bad rings or holed piston. Low oil pressure can be bad bearing or oil pump.

Usually a bad ring or seal inside your engine allowing oil to get into the combustion chamber where the tip of the spark plug is located. Do you notice any smoke coming from the exhaust pipe ?? Do you seem to be adding oil more often ?? If so, the black oily stuff is "engine oil".

You don't mention what that smell is reminiscent of?

You don't mention the colour of the "smoke" and you didn't say whether the engine is petrol or diesel?

You don't mention whether the road behaviour/performance is normal?

White smoke is almost always steam or in the case of a diesel it could be an unburned fuel mist, grey/black is excess fuel and blue or grey/blue is burning oil.

Some steam is fairly normal until the engine and exhaust system is hot but excessive amounts could be one symptom of head gasket trouble. If the engine is drinking coolant and sending it through the exhaust as steam it will sometimes smell spicy.

Burning oil smells a bit like burned eggs in the frying pan.

If the car hasn't ultra-low sulphur oil and fuel the catalytic converter will convert sulphur traces into hydrogen sulphide - the bad egg gas...

Sounds like either a blown motor (rings need replaced) or a bad head gasket or cracked head.
If the rings are bad your car would have felt like it was losing power because the engine will no longer have the same high compression that it's required to turn the wheels. You may have heard your engine knocking or seen a light blue colored smoke coming from your exhaust as a result of your engine burning up oil in the combustion chamber from the rings leaking.
If your head gasket is leaking or your head is cracked you'd likely find milky looking oil when you drain your oil from water/antifreeze being mixed in and noticed a white smoke coming from your exhaust that is actually water vapor coming through the exhaust.
If your car was running rough when you last shut it off try pulling all of your spark plugs and either cleaning them or replacing them all. A bad head gasket or bad rings can both foul spark plugs. A car will run rough with 1 or 2 fouled plugs, but once enough foul it will no longer run at all just sit and crank over. If changing the plugs get's it started for ya, check your tailpipe first for water, if nothing, change your oil. If no signs of water/antifreeze or milky colored oil then it's probably rings.

Take a compression test on # 4. It may be a little oil burning w coolant getting by the head gasket. POSSIBLE faulty injector or not firing on time. Ck for any oil in the anti freeze or anti freeze in the oil.

should be idling roughly
engine check light on ?

faulty coil ok when cold no good when hot

do a compression test on number four
no compression on cylinder four

leaking intake or exhaust valves
the injector isnt working
if everything looks ok and no better
a blown head gasket

check spark plugs and distributor. look for bad wear and missing parts. It must be a faulty spark plug which is not igniting fuel in one cylinder. If you decide to replace the plugs its best to change all of them.

white smoke from the exhaust and overheating would almost certainly mean a blown head gasket.
the head gasket has gone between a cylinder and a cooling channel so exhaust gasses can get in to the cooling system resulting in the boiling and water from the cooling system is getting into the cylinder resulting in the white smoke (actually steam) from the exhaust.
the exhaust manifold is a separate issue that can be replaced when the head gasket is repaired.

when your getting clouds of steam from your exhaust that is a good tell tell sign that you blew a head gasket