It's an informal phrase that might be offensive; use it carefully depending on your company. I wouldn't say your boss is off his nut - that could sound disrespectful.
Pro Tip 2/3
Emotional Punch
The phrase often conveys strong feelings about someone's behavior, usually disapproval or shock. He started dancing on tables; we thought he was off his nut!
Pro Tip 3/3
Not for Formal Use
Avoid this slang in formal contexts; it's suited to casual conversations among friends. You wouldn't tell your grandmother she's off her nut for forgetting her keys.