Oil drilling doesn't occur where the lithospheric plates (the ones that move and cause earthquakes) meet. Most of the plate edges are under too much water to make it practical, and there wouldn't be much if any oil to find, because the plates are relatively thin at the edges.

The deepest oil wells we've ever drilled on land go down about 24,000 feet in areas where the plates are about 150 kilometers thick (through the continental crust). Oceanic crust is thinner, but we can't get very deep into the sea floor because of having to go through all the water to get to it.

Since the mid nineteenth century, world wide we've extracted about 125 billion barrels of oil from the ground, with a total mass of about 16.8 billion metric tons. The total mass of the lithosphere is in the neiborhood of 225 quintillion (that is, billion billion) metric tons.

The plates themselves have never had oil lubricating them at the junctures or anywhere else. The plates float on a sea of what is mostly magma, and shift because of currents in the fluid. Oil is found in pockets in the rock, not in the interstices between plates. The plates are a good three billion years old, whereas oil deposits created from the compression of carboniferous life is more like 300-400 million years old at most.

One way to think of it is that drilling for oil has as much to do with plate tectonics and earthquakes as a mosquito bite does with whether a burrito is going to give you heartburn.