As others have said it's very doubtful that the electricity is causing these vibrations you speak of.
You mentioned your meter box cover has been vandalised, and your electric consumption overnight was excessive. It is entirely possible that the neighbors may have tapped into your supply illegally, unlikely though but not impossible. Contact your DNO Distribution Network Supplier, and the Police.
As for the constant noise which you believe is a looped recording, the Council and the Police need to be informed as well, if you call in the police, you will need evidence of harassment, if you can go to the extent of installing a CCTV camera, covering your house that would be one way of providing evidence, record the noises as well, not just over a day, as the Police will treat it as a one off incident, a longer period of recordings will be required, keep a detailed diary of occurrences, above all try not to antagonize the people next door, difficult I know, but you will only compound the matter if you do,
You could call the council and police now, but without proof there will be little they can do, and next door will stop for a few days to cool off, and then resume with their shenanigans, wait until you have sufficient evidence before you call anyone, hearsay will not wash in the eyes of the Law. good luck, and try not to let the boogers get you down.