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.
Does Cu oxidation away from contact points matter?
I'm thinking specifically of bare copper component leads. If the contact points are soldered, would oxidation along the length of the wire have any appreciable affect on performance? Wouldn't the vast majority of current be carried through the "core" of the wire (that is, everything below the oxidized surfaces)?