off your nana

off (one's) nana

old-fashioned slang Crazy, insane, or mentally deranged. Sometimes written as "off (one's) 'nana" to reflect the abbreviation of "banana." I think you've gone off your nana for giving up that cushy office job, but, hey, follow your dreams. Don't go off your 'nana, I only took the car out for a quick spin. My auntie likes to let people think she's off her nana, but she's actually incredibly clever and witty.

off your nana

mentally deranged. Australian

Nana in these idioms is probably short for banana ; compare with go bananas at banana.