What kind of oil are you using? Synthetic?
Oil burners usually have smoke with a blue-ish tinge to it. White smoke is usually water vapor. Black smoke is unburned hydrocarbons/soot/fuel.
Your symptoms do sound like a broken piston ring (s), though, especially the oily deposits in the exhaust.
Compression check time. Perhaps a bit of crying...
On second thought, check your engine breather system first. It needs to vent to the atmosphere somewhere. Over 5000 RPM is where blowby is likely to occur, which would pressurize the crankcase. This would upset the piston ring seal, among other things.
Cheers,