The USAF and the USN will be tasked with keeping the Gulf open to shipping, a job they did ten years ago with fewer bases and worse logistics. The strategic reserve will be around to pick up the slack in case a tanker or two is caught in the crossfire. Don't bet on an oil shortage.However, I would bet upon a panicked surge in prices for a while. The market price of oil would rise due to traders' fears of a supply interruption.
Give them a few weeks, and prices will come back down to "normal." (I'm still waiting to see gasoline for 99.9 cents per gallon like it was when I was younger...)
The USN will keep the tankers safe. There is no doubt of that.
During the Gulf War prices spiked a little on the day of the first air attack and then fell like a stone and stayed down. The traders run prices up on the news to suck in the amateurs.