Difference between Be off one’s nana and Lose one’s nana

be off one’s nana—(Austral. sl.) be mentally deranged:

• We’ve learned to laugh at our predicament. If we hadn’t we’d all be off our nanas.

lose one’s nana—(Austral. sl.) lose one’s temper:

• Lost my nana with a couple of customers tonight and wish I hadn’t.