"To be off", colloquially used to mean leaving, presently. It's very common in the UK at least.
"So, we've finished? I'm off, then..."
"We're off home now. Bye"
"Got your coat on already? Are you off?"
"Right, I've had enough. I'm off for a smoke/fag/cigarette/tab/infinite dialectical variations..."
"I'm off to walk the dog."
Or in a *slightly* more indirect way, also very common (has a slight sense of additional politeness, I'd say):
"I'll be off"
"We'll be off home now"
Also used to mean off work, as the others have explained. (It is also used to mean 'spoilt' when talking about food, as a variation of 'gone off'.
"Wow. Smell that... This fish is off." - that is, is rancid, is rotten or generally not safe to eat anymore)
"To be out", simply to not be somewhere for a while.
"Can I send a plumber round this afternoon?" - "Not really, we're out" (not home)
"What about Thursday?" - "We'll be out then, too"
"I called your office this morning, you weren't there" - "Yeah, I was out."
(By the way, "to be out" is widely used to mean out drinking, or eating to a lesser extent. As in a "night out". "Are you out this Friday?" - "No, I've been out too much this month. I need a break. I'm skint, anyway.")
This is a good question, these are nice little phrases with many uses.
I've just remembered that the expression,
"I'm off out..."
is also very common here, too. Which is pretty comical. It's used the same way as "I'm off" just with slightly more emphasis on "...outside".