It sounds like you've been pegged as someone who submits spurious complaints. The mayor's office, Attorney General's office, etc. have other things to do rather than respond to such complaints, so you won't get any traction with them. And though it might seem that the police department is required to enforce the laws, they have a great deal of discretion in handling complaints of disturbing the peace.
You could submit an application for criminal complaint against your neighbors for disturbing the peace, or even theoretically sue them for creating a nuisance, but I'm not recommending either course of action. The courts are clogged with groundless cases every year, and you don't want to be responsible for a case that will just be dismissed; it's a waste of your time and public resources.
If you're a tenant, it would be good to start looking for another place. If you're a property owner, it's not a bad idea to consult with an attorney, but based on the facts you've given I wouldn't take any action without doing so.
I agree with Attorney Varszegi. You could apply for a criminal complaint yourself by going to the courthouse for the jurisdiction where you live. You could also sue them for nuisance, violation of your right to quiet enjoyment of your property, etc. But that may not solve your problem. Some people get even more belligerent when they know they're disturbing someone. Could make problems with the neighbors escalate. Try looking for another place.
Attorney Lauren Craig Redmond ~ 617.953.6116 ~ No attorney/client relationship is established or implied by any email or phone conversation.