Osage Orange (aka Bodark down here) will absolutely make the best wood corner post you can get. Once it cures you will have a hard time driving a nail or staple into it. I don't know a specific time for curing before use but would guess that one season is enough? Under a shed would be best but outside would be OK, they're going to be outside when you build your fence. After three to five years they will be like iron. The advice that comes to mind would be to have your sharpener handy, you will go through some blades even on green wood.
Craig-TX