The catalytic converter.
You're burning oil.
Clean the mouse nest out of the air cleaner.
Sounds to me like the clean one is not being used at all, maybe it is a fake dual exhaust. I took that to be that you have duel exhaust, sorry. Sometimes a short drive or several short drives will leave the exhaust pipe sooty black. A good long highway drive will leave the exhaust pipe greyish white. This would be normal.
What can cause black sooty exhaust is bad valve guides. When the guides are bad oil leaks into the cylinder when the car isn't running. When the car starts it produces black exhaust.
It is important to maintain a car while driving or owning one. When a car's exhaust is spitting out black deposits, it is because there is oil in the system where it does not belong.
engine is burning oil could be valve seals or piston rings
Blue smoke means oil. Rings or valve seats. your car is burning oil.
you could be leaking engine oil onto the exhaust or it could just be rusty water that is evaporating and causing the smoke.
Dawn dishwashing shop or brake clean, cherry bomb soap is also a great product
You might have an oil leak that gets on to the exhaust manifold. Check the gasket around the upper part of the engine.
do you mean the EGR valve? The Exhaust Recirculation Valve? EGR