off (one's) nana(redirected from off their nanas)
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 nanamentally deranged. Australian
Nana in these idioms is probably short for banana ; compare with go bananas at banana.