Do the three phrases convey the same meaning when we're referring to the place where one lives?
As long as the context is clear, then yes. But context is very important.
Examples where they would not have the same meaning:
Names of bars, clubs, etc. "We're heading down to O'Connelly's tonight; care to join?" or "They met at Meg's."
Or basically any other kind of proper noun.
Again, if the context makes it clear that we're talking about residences, you're golden.