Sometimes not always - puff of smoke when starting ( light colour) followed by lumpy tickover and noisey clacky sound from engine - all becomes ok when warm

When the head gasket fails on a liquid (water) cooled engine the typical smoke colour is white (steam) and that becomes rather underlined by the steady drop of the coolant level and often clear evidence combustion gas is leaking into the cooling system.

Smelly black/grey smoke tends to be produced by an over-fuelling condition such as a stuck choke or strangler or other cold starting aid or perhaps carburettor flooding.

Blue or blue/grey smoke is invariably engine oil burning but I suggest you ignore that until the black smoke problem is rectified and after a short time the blue smoke might also disappear. If it doesn't it could be related to the overheating but the black smoke probably wasn't caused by that...

try disconnecting the battery for a hour and reconnect it this will resest ur ecu unit and 9 times out of 10 fixes it hope it helps

I have seen this on old cars, my suspicion is that the seals on the valves are a bit worn. This allows some oil to get through during start up. Since it quits smoking, I would not be overly concerned. However, since it burns a quart every 1-2K miles, I am curious what the compression is. My Fiero does the same thing (occasional puff of smoke on start up) but does not need oil between 3,000 mile chages. It is a 2.5 liter. Here is nice tip: check compression on all cylinders, then recheck it adding a teaspoon of 2 cycle oil to the cylinders (one cylinder at a time). Some have said to use conventional oil for this, due to higher viscosity, but I always thought it might foul the spark plugs. If the compression goes up, it is ring wear, if not it is leaking through the valves.

bad water pump maybe

i have found 2 areas that cause issues such as you are reporting.
one is poor voltage. check the connection at the starter motor between the alternator and the battery.
the other and perhaps more likely is a wet ECU.

the ecu box is under the windshield on the passenger side, access under the hood. this are can get wet ad corrode an ECU.

remove the ecu, take the bottom plate off and clean any corri=oded and wet areas with alcohol and a tooth brush..be gentle.
i would look for a way of mounting the ecu so that it doesn't lay on a flat surface that gets wet...

If the car starts again without trouble - it is probably an air leak on the inlet manifold or associated pipework. If the car is very 'lumpy'' then stops it could be a coil-pack or mass airflow assembly - also this fault sometimes triggers a gearbox fault warning as the engine and gearbox become out of sync. due to engine misfires.
The air leak fault will not always register in the fault code memory of the car whilst in its early stages. As the fault becomes greater - the engine will become hesitant - then stop. This is the time to spray leak detector spray around the pipes or manifold joints, as the spray gets 'sucked' into the leak and the engine note will change noticeably.
Hope this helps - good luck.

sounds like its out of time at the injection system and or engine timing

It sounds like a piston oil ring is broken considering the valve stem guides and seals have been done, oil is definately getting into the combustion chamber there are only two places that can happen through the valves or through the rings, black smoke is always too much gas, blue smoke is always to much oil in combustion chamber. Hope this helps even though it's not the best news.

A puff of smoke when you start up indicates worn valve seals.That's why all your work didn't fix the problem and it doesn't show a code. It's a pain in the --- job that requires some specialized tools so I guess it depends on how bad it bugs you,if oyu want to fix it.

1. My suspicion is your electronic ignition
2. If your car is a bit old, there might be a leak through your valves
3. Distributor timing gear is damaged (replace)