Do we need to keep the oak leaves off our st Augustine grass

If it is winter weather where you are, it won't hurt it to leave it while the grass is dormant for the winter. I would remove it before the grass comes back to life in the spring. If it is thick the leaves will keep out the sun and you will have bare spots there. If they are dry it would help to run the lawn mower over it to shred the leaves if you can't remove them soon enough. We boo boo'd one year, we had been raking and had them in piles when it started to rain. It froze overnight. By the time the piles had thawed enough to remove them, the grass underneath was already dead.

If you're going to run the lawn mower over them why not use a bagging mower and dump them in garbage. recycle or compost pile or which ever method is available to you. You won't have to deal with them later.

It is best to trove the leaves to avoid fungus

If you don't collect them to use as garden mulch or compost, using a mulching mower is best. As others have said, leaving them on top of the lawn will kill the grass due to lack of sunlight.