Car is a 6MT, has over 100K miles and I haven't driven it much in the past 10 months or so, just to the corner and back every 2-3 weekends. I recently changed the oil (good Castrol EDGE 5W-30 high mileage full synth), but forgot to use the use the washer in the screw that plugs the tank exit, so half of it dripped out. With little to no use, I still went ahead and dumped that oil and completed a full change again just yesterday, with filter replacement. After confirming I have the right amount of oil (right at the MAX mar), I took the car for a short 1/2 mile spin and when I got back and out of the car, I smelled something burning. I don't know exactly where it came from, which is why I'm coming to the experts. Any idea where to look? Again, the fact that the car has been sitting for so long should be key here. It also hasn't had any maintenance other than the oil change in at least 40K miles. That's definitely another factor.

EDIT: I went for a short drive so that I could take photos and a video of the smoke that comes out from behind the engine more on the passenger side. Hopefully, this helps narrow this down. See them all here: https://imgur.com/a/gkpW0u0

 

Looks like oil burning off from a leak to me. With out that cover off to look at it more closely you can only guess. If it has been sitting and leaking oil you may have oil on the exhaust that needs to burn off.

 

I'm pretty certain the oil leaked only from the bottom of the tank where that screw/plug goes. And that goes straight to the ground, since there's nothing below it. I say this because there was a huge oil stain right under it and not even one drop since I changed it again and used the washer, which I forgot last time. See what I mean? See this photo (not my car) for an illustration. Any other ideas?

 

I was not referring to your drain oil leak I was referring to a VC leak or from somewhere else. That's why i said the cover would have to come off to get a good look at what's going on back there.

 

I must have misunderstood. Since I had said I know the oil leaked out and I know where it leaked from, your statement "If it has been sitting and leaking oil" to me was referring to THAT leak. Prior to that leak or sitting for months, my car wasn't having that smoke or burning smell.

 

Oil on exhaust from the valve cover is a common problem
Goos

 

Which valve?