Oil Pòr the escape?

Hi, I have a 2004 Volkswagen Caddy 1.9 TDI 105hp.
For some time now, there's been a smell of burnt oil when I stop the van suddenly. I was overtaking at 2500 rpm when the fuel injection cuts out. I took it to the mechanic, and he told me the turbo was overboosting and cutting the fuel injection to protect the engine. He said the solution was to replace the turbo, but suggested cleaning it with a spray that was probably just carbon buildup. I kept the van for a couple of days, and he told me to test drive it. I did, and it produced a lot of white smoke and a burnt oil smell, which I thought was the spray burning. As the days went by, the smoke increased, so I decided to replace the turbo.
He replaced the turbo, disabled the EGR valve, and the van ran perfectly. The fuel injection no longer cut out, and there was no more smoke. I thought, problem solved.
After a few kilometers, the malfunction indicator light came on. I took it to the mechanic, and it turned out the ECU had detected that the EGR valve was disabled. He thoroughly cleaned the EGR valve, and it opened and closed properly. He removed the small plate, and it seemed to be working normally.
To my surprise, shortly after starting the engine again, there was a little white smoke, and worse, when I stopped at a traffic light, a huge cloud of smoke—I was so embarrassed! People were telling me the car was on fire. Well, when I accelerated, it decreased and almost disappeared until I stopped at another traffic light.
I suppose it was when the EGR valve opened, so I disconnected the EGR valve's opening hose, and that solved the problem—no more smoke.
The mechanic wants to replace the EGR valve, but I doubt it's the EGR valve because, as I understand it, oil enters through the EGR valve's exhaust pipe inlet. If the engine were burning oil, it would always smoke, not just when the EGR valve opens, which is when I assume oil is being forced into the intake.
Question: Where is the oil entering the exhaust manifold? Could it be an exhaust valve, or perhaps the new turbocharger?

Oil can get into the engine for several reasons. The first, as you mentioned, is the EGR valve, but it can also happen through the head gasket, valve stem seals, and piston rings. What you could do to test this is remove the EGR valve and replace its gasket with one you make yourself from a sealed material. This will disable the EGR valve but keep it connected so the computer doesn't go into emergency mode. Test it and let me know how it goes.

The function of the EGR valve is to allow exhaust gases to pass into the combustion chamber to lower the chamber temperature. Oil cannot pass through the EGR valve because it only connects the exhaust to the intake. First, you should check if your engine is consuming oil. This should happen over the course of a week. If so, you may have oil passing through the valve guides. Oil typically accumulates at low RPMs, and when accelerating, it emits a lot of smoke, which then diminishes. The turbocharger could also be the culprit. This can be checked by removing the hose from the intake manifold to the intercooler. If oil is passing through, you will find oil contamination in those lines. If there is no oil consumption, you may have problems with excess fuel or an injector that isn't sealing properly. There are several possible causes.