Think auctions.

Oil is priced in dollars. Assume that yesterday, the price of oil is the same as it was yesterday (e.g., $70). Assume you need 10 barrels - $700.

Finally, assume that today, the Euro appreciates against the dollar. One Euro buys more dollars today than it did yesterday ($1.40, vs. $1.30). What happens to the oil price?

Yesterday you needed (EUR)538,46 to buy your 10 barrels. But now you need fewer Euros to buy the same oil: (EUR)500,00. You save almost (EUR)40! If you get paid in Euros, it appears to you that oil is cheaper than it was or yesterday.

If EVERY major currency buys more dollars than it did last year, oil is cheaper everywhere than it was yesterday. Everywhere, that is, except the US, where the dollar price of oil is the same.

But if oil is cheaper, people can use more of it (and more people can use it). Some of those Europeans who are saving money on oil will do something to use their savings - and some of those activities will require more oil. They may go on a vacation (jet fuel? road trip?), or buy imported goods (transport).

Here's where the auction comes in. Oil goes to the highest bidder. In our scenario, Americans in the oil market are paying what they paid yesterday. Europeans, however, have that extra money to spend on energy - so they bid up the price of oil. Many Americans still need the oil for commuting, fertilizers, trucking, etc., so they pinch pennies (clip coupons, cancel Christmas, whatever) and spend more on oil than they did yesterday. Other Americans either can't afford to spend much more, or choose to conserve in the face of higher prices.

End result: dollar price of oil goes up. Europe gets more oil, America gets less.

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I hope this answers your question.

As for the difference between Brent and WTI, both of those prices are in dollars. The difference has to do with the quality of the oil being contracted for (is it "sweet light", or a more "sour" crude?), and the transport costs to get the oil delivered to the designated market site.