I would start with a compression test to make sure the engine is in good mechanical condition. If there is a compression loss it can cause issues like what you’re experiencing. If the compression is good, then I’d be looking at the fuel system. It seems to be running rich for some reason. It could be a leaking or malfunctioning fuel injector.
More info on solving problems like this here: http://www.ericthecarguy.com/faq/solving-automotive-performance-issues
Good hunting and please keep us posted.