Off out isn't usually said on its own. It's usually "I'm off out" or "Are you off out?". It is a phrase that means "I'm about to go somewhere".
"I'm off" means I'm leaving and going somewhere... Eg, you are going to work or to the shops and you say to a person you are with "Right then, I'm off!" meaning I'm leaving now (at this moment).
E.g You visit your friend and have a cup of tea (a cuppa) and and a chat and now it is time to leave - you might finish your drink and then say "OK, I'm off! Bye!" And then you would leave.
"I'm off out" is slightly different. It means you are going out but more of a sense that you will not be in the place you normally work/live.
E.g. you are at work and your colleague asks "what are you doing tonight? Are you staying at home and watching the T.V.?" You might reply "No, I'm off out tonight. I'm going to that new restaurant!"
Or you've been at work all morning in the office and you need to go out to get something from the shops. You might say to a colleague "I'm off out now. Do you want anything done before I go?"
Hope this is of help.