German Brewing

I live in an area of the country where we have distributors who don't care at all about freshness or ensuring beer is kept fresh or cold.

I just moved here last summer, and fortunately am moving to california this upcoming June. I can only hope the situation is better at that time.

Whether it's 6 month old Paulaner, 2 month old SN Kellerweis, 3 month old Weihenstephan, it's very rare I find a hefeweizen that not only has the banana and clove flavors intact, but also doesn't have an odd off flavor as well.

What am I tasting exactly? It's not skunkiness, and it's not outright gross, but almost like the beer is stale. Is it oxidization? That seems odd considering I don't get this from other beer styles of this age. I'm curious to the mechanisms behind this problem.

While I can't say definitively that you are tasting oxidation, my gut says "yes".
An odd bitterness, coupled with muted cloying sweetness?

Not any sweeter than usual.

The flavor reminds me of a crappy light lager in a way, almost vegetal but doesn't taste corny. It's not overwhelming. Seems to happen to every hefe, regardless of origin.

Also of note: Many will lose their cloudiness, but not always, even with proper pouring.

From which breweries are these Hefeweizen? Some bottle condition, so O2 won't be a problem. But badly stored beer deteriorates faster.

It is probably stale malt and oxidized crystal malt. Bottle conditioning only consumes the oxygen in the bottle during carbonation and attaining EVG. After that, yeast are dormant (or dead) and cannot protect against the ingress of oxygen from temperature fluctuations causing air to flow in and out under the bottle cap due to pressure changes and will ultimately contribute to staling.

Unless they are temp controlled the entire time they have them, it's likely.