Most likely it'll be like todays action; Gradually up, then a pop when the rumour gets around enough, then a gradual selloff in the next severaldays after earnings announcement. That's pretty typical for most stocks. Of course, I'm assuming that they'll report decent earnings.
I used to be a vendor to XOM as well as the majority of Big Oil in the US. I know them to be one of the most ethical and honest companies I've ever worked with. They would never allow gouging at the pump at their stations.