If you are off something, you have stopped liking it. I'm off coffee at the moment Diarrhoea can make you feel weak, as well as putting you off your food
If someone is off something harmful such as a drug, they have stopped taking or using it. She felt better and the psychiatrist took her off drug therapy
{e} from; up from; so as to get out or come out of (bus, train, etc.); reduced by (e.g.: "This week all the shirts are 10% off"); so as to get rid of or remove something (i.e.: "The stain will come off your dress")
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If you live off a particular kind of food, you eat it in order to live. If you live off a particular source of money, you use it to live. Her husband's memories are of living off roast chicken and drinking whisky Antony had been living off the sale of his own paintings. = on
If something happens on and off, or off and on, it happens occasionally, or only for part of a period of time, not in a regular or continuous way. I was still working on and off as a waitress to support myself We lived together, off and on, for two years