Given that the oil cap is free from mayonnaise the headgasket's integrity seems fine. It almost looks like someone put oil in the expansion bottle mistakenly at some point? If the HG was gone, you'd have the same build up under that and you'd notice the exhaust smoke had a white tinge to it.

Flush the cooling system thoroughly, and fill it up with new coolant/water mix. Run it for a day, and then check.