How long will oil continue to smoke on an engine block after a large spill?

Wash it down with a degreaser, might speed up the process

Here's what you do.

Start it up and let it run for a while, then shut it off and let the engine cool down completely.

The oil will gel and become sludge, and at that point will cease to smoke as much. You might smell it for a couple of days, but it shouldn't smoke as much, if at all.