Source: American Petroleum Institute (www.api.org). Figures are based on 1995 average yields for U.S. refineries. One barrel contains 42 gallons of crude oil. The total volume of products made is 44.2 GALLONS - 2.2 gallons greater than the original 42 gallons of crude oil. This is called "processing gain," where other chemicals are added to the refining process to create the products.

Petroleum has a specific gravity of 0.88 which means 1 litre weighs 0.88 kilograms.

From the volume page we know that:
1 barrel [US, petroleum] = 158.9872972 litre

So 1 barrel weighs:
158.9872972 * 0.88 = 139.908821536 kilograms

1 metric ton is 1000 kilograms:
139.908821536 / 1000 = 7.1475121

So there are a little over 7 barrels of petroleum in a metric ton.

This is assuming that 0.88 is the correct specific gravity. Since as you said, the grade of the oil may make a difference. If you know the exact specific gravity of the oil in question, you will get more accurate results.