As I understand it, the tannins present in both oak and grape skin serve to act as a buffer (not in the strict chemical sense) against oxidation, being oxidised preferentially before the flavour and aromatic compounds in the wine. This is in part why tannic wines soften with age, and wines with little initial tannin do not necessarily age well. Acidity (and sugar levels?) play a complementary role here as well as clearly there are plenty of white wines that have very little tannin from either oak or skin that age extremely well.
As for your port barrel, and how much flavour it will impart, it will depend on the age of the barrel and how much port has previously been through it, and whether it has been scraped to expose fresh wood if it has been used before. If you like smooth, easy drinking ports, I suggest just buying a brand you like and knocking it off. Aging it in oak may not necessarily produce a wine that you like, though it is great (if not a little dangerous if you have self control like mine) to have booze "on tap". I would recommend topping up with a decent quality, sweetish brandy (most good aussie brandies fit this mould) as a bit of extra alcohol should help protect the port.
But I have never done any of this before, so don't take my word for it!
...and anyone else on this forum who can see anything I have written that is utter crap, please don't hesitate to point it out, and mock me mercilessly