According "The youngest natural oil on earth" Doklady Chemistry vol. 438, pages 144-147:
Prior to this paper, it was known that oil of the Guaymas basin is from young sediments and is 5000 years old.
However, their work shows that oil in the Kamchatka volcanic area is "less than 50 years old". Oil is shown through carbon dating to have formed between 1962 and 1973.
At the opposite extreme, this 1986 New York times article reports:
A team of geologists working for the Australian Government's Bureau of Mineral Resources reports in the journal Nature that it has discovered oil formed from the decayed remains of organisms that lived 1.4 billion years ago, when the earth was young. After the group drilled a 1,100-foot-deep test hole beneath the McArthur Basin in northern Australia, the oldest oil of its kind ever found bubbled to the surface.
Tiny amounts of oil as old as 3.2 billion years have been found more recently.