I'm not as familiar with poison oak as I am with poison ivy but I'll give it a shot. Poison oak can vine just like poison ivy so I would assume that you need to make sure that you remove the root. I've had plants (poison ivy that is) come back even after I brushed on a plant killer on the exposed root (I tore out what I could). What I don't know is what Brush-B-Gon leaves in the soil. If you feel confident that the Poison Oak plant is dead, then one would assume that you could plant in the same soil. BUT Brush-B-Gon is toxic to a number of plants and there is nothing in the Ortho literature on the bottle which implies that the chemical breaks down over time. In fact, they explicitly state that this product should not be used around ornamentals, fruit trees or vegetable gardens. This to me would imply that something is left in the soil. Whether its good or bad? I don't know. You might see if there is a place to ask the question on the Ortho website.

If it were me, I'd probably replace the soil and start fresh. That way you're sure the poison oak plant is gone and the soil is clean and ready for your new plantings.