SBC smoking?

[itsals1]

Well this is in my Father's Chevelle. It has the factory 307/powerglide combo has 89,000 original miles. Has Edelbrock carb and intake, flowmaster dual exhaust,no x or cross over. The engine starts and runs/drives good,BUT when you accelerate it smokes out the drivers side tail pipe, to the point That oil is dripping out of the exhaust? The engine does not knock or make any unusual noise at idle or short revs. He had our local mechanic look at it and he's just not sure as it acts like a broken ring,but makes zero noise? I'm not a engine guru so thought I would ask to see if anyone may have some sort of ideas?

Thanks
Travis