For an oatmeal stout, or any stout for that matter, I would not use sugar. Or maybe I would, but only if it's a dark invert sugar. But that's neither here nor there. To me, an oatmeal stout is rich, smooth, with some chewy texture to it. Adding sugar will push the beer towards the opposite area.
As far as the difference between DME and LME? I wouldn't say one is superior to the other. Only real issue with LME is freshness, as it will stale much more quickly than DME. If it's fresh, though, they're pretty much equivalent. You need to use a bit more LME to hit your gravity due to the water content in it, but that's easily calculated.
You're going to want to do a partial mash with the oats, though, to get some conversion. Otherwise you'll just extract starches.