Personally I wouldn't recommend it why not use a stump killer on the remaining roots?

Unless the roots are entwined around a vein of coal it will never get that deep. Moon growe has the most practical and successful answer.

I wouldn't recommend burning due to its high toxicity. The smoke from this bush is deadly. Mg has a good suggestion. You can pick up stump killer from the garden center at The Home Depot, Lowes or Ace Hardware.

And usually, once you get a foot or two deep, Oleanders won't re-sprout anyway. If you want to plant anything in the same spot, you will need to remove all of the dead roots in an area two feet deep, and four feet wide, or the fermenting dead wood will kill the roots of the new plant in the summer.