Does Cu oxidation away from contact points matter?

Well I've found that the latter principle is bunk due to the skin effect, but even if current is pushed to the surface of the conductor and there is a layer of essentially non-conductive oxide on the surface, wouldn't the vast majority of the current flow in the copper metal just below the layer of oxide? That is, shouldn't the wire then essentially act as a slightly thinner gauge wire where the dielectric surrounding the conductor is copper oxide instead of air?

Copper oxide "patina" is a very thin (about 0.005") and protects itself from further oxidation. Some current would go thru this layer (that is semiconductor) but majority of the current would go thru the core. I wouldn't worry about it at all. Stranded wire situation is a little bit different, because strands are much smaller and, in addition, current will jump from strand to strand (skin effect) crossing copper oxide layer each time.

Cupric oxide has a diode effect and should be avoided. If the cable has any "green" creeping down the insulation, toss it. Jallen