Losing oil, no puddle underneath, running hot, added oil, now running cooler, now burned oil smell.?

noticed car sounded like it was in wrong gear and running hot, checked oil,it was low. Haven't noticed any leaks or puddles where we park, added oil and it was running cooler, but had burning oil smell. what could cause this? and what should I have checked out?Losing oil, no puddle underneath, running hot, added oil, now running cooler, now burned oil smell.?
check the valve covers .. oil can leak out and go on the exhause manifold and burn.. you need to replace the gasket is this is so.. when you have the cover off you will see a troth on the low side that leads to a hole this is the oil return to the crankcase.. take a hanger and cut the top off and unbend it place this in the hole and gently push it to make shure it is not plugged. this also can cause oil to leak ok..Losing oil, no puddle underneath, running hot, added oil, now running cooler, now burned oil smell.?
Check the maintenance history of the car.
check the valve pan gaskets, they might be leaking oil down on the manifold and burning.
look under the car not at the ground but the under side of the motor ... check your valve covers the top of the motor,,, the tail pipe.... you smell oil either you spilled some when adding or you have a leak
Check your coolant tank or radiator. If you are losing alot of oil and do not see a leak it may be leaking into the coolant. Also look at the color of your oil if it looks like chocolate milk you have a head gasket problem. Possibly your coolant is low and the new oil cooled your engine some so it ran cooler. After that take it to a qualified rechnician if none f those things are visible.
If you spilled some oil on the engine's exhaust manifold while adding oil, it will take a while to burn off and you'll get that burning oil smell and smoke.