"How does defense affect a pitcher's OAV?"
To answer this question, we must first understand there are two parts to this question, and how the question is sort of the wrong one.
Team fielding affects OAV not at all. Errors are not charging the pitchers with hits. They can lead to unearned runs, however. Unearned runs can cause you to lose more games in ways that aren't reflected anywhere else in a pitcher's stats, but so can your own failure to score runs.
Team range can affect OAV a marginal amount. A (+) play erases a hit, and a (-) play creates a hit. Thus, good range leads to lower OAV and bad range leads to higher OAV.
"How much does a good defense help and a bad defense hurt...?"
100 different owners will give you 100 different answers. I'm probably on the lower end of defensive impact belief, but as someone that's not me you definitely shouldn't just take my word for it.
"...and does a pitcher's strikeout rate rise in importance with the defense behind him is poor?"
Sort of, yes. Understand how the event tree works. I'll show a simplified version to show just what's relevant here:
1) Let's start by assuming an out is determined. Obviously, not all PAs are outs, but we only care about ones that are at the moment.
2) This out is decided to be either a fly out, ground out, or strikeout. A pitcher's strikeout rate is relevant here. Not sure what goes into ground vs. fly exactly, but the K-rate is definitely used to determine strikeouts. So a pitcher with a high-K rate will have more outs be strikeouts.
3a) If an out is a ground or a fly, it is put in a place on the field. A fielder must then try to make a play on the ball. In most cases they will, but there are small chances (that go up if the fielder is bad) for a (-) play or an error to allow the runner to reach base. Then record the out or baserunner advancement, then proceed to cleanup step. (If applicable, double-play and triple-play opportunities also show up here, but to detail this likely confuses the issue.)
3b) If an out is a strikeout, we record the out proceed to cleanup step.
So if you have bad defense, good strikeout rates minimize 3a) triggering at all and thus the chances for that bad defense to hurt you. But that's only a select number of outs, because no pitcher has perfect K-rates.