Q: Burning engine oil and have gray smoke coming from below the engine and the tailpipe.

Hi there. If you are getting gray smoke from under the vehicle and in the engine compartment, then there is an external oil leak. The oil is leaking onto the exhaust pipe and then burning off. This is why you are not seeing any oil on the ground. As for the engine smoking some oil, then the valve guide seals on the cylinder heads are possibly leaking causing oil to enter the combustion chamber through the intake valves.. Another way that the engine could be getting oil into the combustion is having a positive crankcase ventilation valve (PCV valve) being stuck causing oil to enter the intake system. To check this, check the intake tubing and see if there is any oil present. If there is oil present, then I recommend replacing the PCV valve to prevent any oil from going into the combustion chamber. The external oil leaks could be, a leaking front engine seal, a leaking rear main seal, a loose oil filter, oil cooler lines could be split or loose, or a valve cover gasket could be leaking. If you need further assistance with your engine using a lot of engine oil, then seek out a professional, such as one from Your Mechanic, to help you.