2006 Chevrolet Epica Smoke coming from exhaust pipe

Did you replace the valve seals when doing your overhaul?

About the valve seals, yes they were replaced during overhauling.
History:
Before the car has been scheduled for ovehauling, these are the signs:
1. When rev at higher acceleration, black smoke is coming from the exhaust and significant reduced in engine oil.
2. During idle, white-blue smoke was also there.
Right after overhauling and break-in at idle speed, no black smoke has been observed. But when accelerated, heavy cloud black smoke is there to the point that excess gas also mixed with engine oil leading to the busted spark plugs (heavily carbonized). Replaced the exhaust O2 sensor and the spark plugs. Heavy smoke has gone. What remains is little black smoke coming out from the tail pipe when highly accelerated, but no signs of failure detected from scanner.

When you plug in your scan tool. Scroll around and look at all your temperature values such as engine coolant temp sensor (ECT), intake air temp sensor (IAT), and ambient air temp sensor to make sure everything reads correctly.

Thank you sir.
I will do it as soon as I can and will inform you back.

Just checking in on your progress. Any luck with the issue?

Sorry for the late reply...

Yes Sir, the coolant temperature sensor is at fault. Replaced it immediately and the slight black smoke coming from the tail pipe during high rev has tremendously gone.

Thank you very much, :)

Great! That's really what I was shooting for, but I wanted to make sure they were all in good working order. Happy to help!