The Law of Supply and Demand is a fundamental driver of almost every commodity, If we treat Oil and Dollar ( Currency ) as commodities it would be simpler to explain their price movement using the law of supply and demand.
The answer by Josh Velson on Strong Dollar Affecting the Oil Prices pretty much sums up a very nice point on relation of Stronger Dollar and the Oil prices. Since currencies have relative strength or weakness, strengthening dollar would make other currencies relatively weaker.
An article published in The Wall Street Journal mentions about Oil supply glut and relative strengthening of US Dollar by FED likely to raise interest rates in June, If so it would be expensive for other countries to purchase Dollar, simply they would require more of their currency unit to buy one dollar, this will likely put pressure on Oil players to reduce oil price in dollars.
Analyst fears about Oil supply glut may build quickly after some of the player which has stopped oil production due to outages, relatively strengthening of US Dollar may also pose a falling trend to Oil prices. Oil has tested $50USD/bbl, which is high in 7 months, and could remain in this levels if supply concerns fade, but likely to be affected by any decision of Interest rates hike this June.