How many barrels of oil make one metric ton?

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

From the volume page we know that:

1 barrel [US, petroleum] = 158.9872972 liter

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.