On the question of whether a) oxidized and b) corked wine can be used in sauces, IMO you might get away by using (slightly) oxidized wine but you are most unlikely to get away with using corked wine. The reason is that in the case of oxidized wine, a small amount of vinegar is present along with the wine. This vinegar may or may not affect the taste of a given sauce depending on the degree of oxidization, how light the sauce may be, etc. I do agree with those who stated that using oxidized wine in stews does not seem to show any adverse effects. After all variants of stew recipes call for vinegar rather than wine on occasion.
Corked wine is a very different matter. It has a very disagreeable flavour because the cork used to cap the bottle was not inert as it was supposed to be but had substances in it which were leached into the wine giving it a very bad taste. This taste is definitely not the taste of vinegar. It should probably destroy the taste of any sauce especially the lighter ones. It is not too hard to even alter the taste of spicy stews.
The proof of the pudding is in the eating!