White smoke from the engine

OK, since you didn't mention a make model, year or number of cylinders this is just an old mechanics take on the situation. Blue smoke on deceleration (closing the throttle) is because of high vacuum in the cylinder pulling oil past either the piston rings or valve seals. Usually, blue smoke on a cold start is caused by the valve seals leaking into the cylinder while the bike is sitting. A quick check to see if the piston rings are at fault would be either to come down a long steep hill or accelerate hard then close the throttle, if it emits a sizable amount of blue smoke when you open the throttle again, the rings are most likly at fault.
The oil getting black is it doing it's job of keeping the engine clean, and the oil consumption you mention would not necessarily be cause for concern on an air cooled engine, especially in a warm climate. Is it possible this condition existed before all this work was done? If so, I'd suspect a carburetor problem, an over rich mixture, possibly because of a faulty float valve or the float itself contaminating the oil with raw fuel, especially if the bike is left on the side stand without the petcock being turned off.
To sum things up, a leak down test will show the condition of the rings and valves. Also might mention that if newer type (usually blue or green color) valve stem seals were used, there is a special procedure for installing them not all mechanics are aware of. The valve must be put in the guide first and the seal worked over the stem with the thumb then it can be tapped down onto the guide. Hope some of this helps, Frank

Usually zmr dont have these kinds of problems.your engine bore is gone thats why your engine oil level is reducing.and the black smoke is coming out...usually these problem occur when you are travelling in higher rpm at lower gear...

Are you getting any smoke from your exhaust. White smoke.
If your intake manifold is leaking coolant It will not appear in your oil.
Hope this helps.

Seems like it has a bad gasket in the engine.
The engine may have damage if it smokes.
Is the smoke white or blue?

White smoke usually occurs when there is not enough heat to burn the fuel. The unburned fuel particles go out the tailpipe and typically produce a rich fuel smell. It's not unusual to see white smoke in the exhaust during cold weather until the engine warms up.

Faulty glow plugs or control module can cause white smoke on engine start up.

Low engine cranking speed may also produce white smoke.

If white smoke is still visible after the engine has warmed up, the engine may have one or more bad injectors, retarded injection timing or a worn injection pump.

Low compression or air in the fuel system can also be a source of white smoke.

With regards to the above problem, I have just recently experienced the exact same thing with a 98 Mazda Bravo b2500 (this is a diesel).The symptoms were after driving over some corrugated dirt roads the vehicle would not rev over 2000 rpm and at that point would blow heaps of white smoke and misfire, but would idle beautifully and rev smoothly up to the 2000 rpm. Also noticed when vehicle was cold it would drive good for about 5-10 mins then symptoms would start again.

Fuel filters were changed, sediment trap cleaned,different fuel tried and checked all lines and system for air entry, problem still persisted. While checking injector pump lift pump pressure I noticed that the pressure would drop right off at the 2000 rpm, maybe a lift pump problem?? After consulting the workshop manual I found there is a small stainless steel thimble filter under the injector pump fuel line input union bolt, held in place with a small spring. Pulled this out to have a look and it was full of crud, cleaned it all up and put back together and have a guess what......goes like a brand new truck!!

Cheers