out means fuori and off means dalla in the sense of levarse
take means portare
take out means portare fuori:
We wouldn't like to eat at the restaurant, we'd like to take or food out.
could you please take the dog out? It's time for her walk.
have you taken the rubbish out today?
take off means staccare / rimuovere / cancellare
I don't like that painting, please take it off the wall.
It's hot in here, may I take off my jacket?
We did not order nor consume a bottle of wine. - Our apologies, I shall have it taken off your bill immediately.