The biology of such a creature is plausible - oil is an energy-rich substance and there are bacteria that can digest it. These creatures may have a symbiotic relationship with such bacteria. The real question is why they would be intelligent.
Most intelligent animals eat a wide variety of food sources (they need to learn which are good for eating and which are not, and remember the tricks for eating each kind of food) and many are carnivorous to some degree (they need to outsmart prey). Grazers are rarely very intelligent, and sucking on oil wells seems to be pretty similar to grazing. However, there is one intelligent species that may have evolved with an ecology similar to your oil-eaters: Elephants.
It is theorized that elephants evolved their substantial brains not so much for the sake of finding food, but for finding water. When resources are rare, far apart, clumped together, and tend to vary in how accessible they are (pools appearing and disappearing seasonally), it is important to be able to remember where those resources are in order to migrate between them. It is also important to remember what conditions are associated with the appearance or disappearance of a given pool (heat and rain). A social hierarchy may develop as herds migrate together, and older individuals may remember pools that younger ones do not.
An analogy can be made between elephants searching for water and these sea-creatures searching for oil. Oil wells are rare and far apart, and many are fed from deeper sources or shale that slowly replenish the easily-accessible reservoirs over time, at least until the deeper wells are depleted (presumably the biological mechanisms of these creatures are not quite as effective as the best human equipment, so they are only able to access the most easily-accessible wells). Finding new oil wells is difficult (perhaps the creatures have some kind of natural sonar ability) so being able to remember to return to the old wells decades later will be a major survival advantage, as will judging how quickly each well tends to refill. As with elephants, this will likely result in a complex social hierarchy with elderly leaders that remember the old wells, migrating in huge herds across the ocean floor.