Why is there a noise coming from the electrical box after turning off the main breaker?

There should be no noise caused by loose electrical connections if the main breaker is off. The only places that are energized at that point are the main lugs. There is nothing running so there shouldn't be any current which is the only reason a loose connection can cause noise.

But all that is based on what SHOULD be happening. If someone has tied into the mains to feed something then there could be noise caused by loose connections. Another possibility is something mechanical causing the panel to vibrate. Tightening the mounting screws might be sufficient to solve this problem.