I'll give it a try. Assuming oil is what is being burned and the plugs are fouled with oil (smell them), it may be valve guides/seals. While the car is sitting overnight, oil may be able to find its way into the cylinder(s) via gravity and a faulty valve seal. I'm no expert, but am grappling with an oil consumption problem as we speak. I just finished pulling the intake manifold to see if oil is making its way past the guides and into cylinders under vaccum conditions. There is likely a way to determine where its coming from in your case, keep asking. Board will liven up tommorrow.
Good luck,
Dave M