The net effect of the weak dollar is a higher price at the pump. Yes, there are many other factors, but the dollars fluctuation is not "irrelevant" in a world traded commodity.
World trade on oil barrel prices is in USD. It is what it is at closing bell.
If shell in Norway or where ever wants to pay for it in Euro's, big deal, it doesn't effect our pump price. just the barrel price which is in USD does.
Now, as I mentioned, IF oil was traded on the world market in Euro's, that would have an effect on our dollar, because it would no longer be the world standard for trade. It would probably slip, and the euro would climb, which has both pro's and cons for them, just as a low dollar would have pro's and cons for us.