I do not see what you would sue for. This does not rise to the level of harassment, or any of the other headings you've tagged based on what you have presented--more facts are needed. However, since you say you're not even home during the purported noise activity--have you explained that to your landlord? If so, what was the response? Also, when you say "serve" do you mean you've been served with legal papers, or are you just talking about correspondence from your landlord? Also, what kind of noise is this? For example, if it is a dog barking, you don't need to be home for your dog to bark. If you have had discussions with your landlord and they haven't gone anywhere, then get a local lawyer to send a legal letter on your behalf to the landlord, explaining your position, and also that any further complaints have to be sent to your attorney--that usually gets their attention, and they may tend to be more judicious on what they send. Keep in mind if you're on a month to month or your lease term is otherwise coming up, your landlord can simply decide not to renew with you.
We do not have an attorney-client relationship. I am not your lawyer. The statements I have made do not constitute legal advice. Any statements I have made are based upon the very limited facts you have presented, and under the premise that you will consult with a local attorney. This is not an attempt to solicit business. This disclaimer is in addition to any disclaimers that this website has made. I am only licensed in California.
There is no cause of action that would be recognizable in court. As to that fact that you were not in the unit on the dates of the complaints, I would differ with my Irvine colleague and keep that to myself, making sure I had something, like a receipt for drinks, stapled to the noise complaint. In the event these noise complaints turn out to be 3 day cure covenant or quit notices, or for the basis for them, I would disclose the evidence that the notices were works of pure fiction just before trial when there is a standing order to exchange evidence.
A proper response would require a thorough investigation into the history and background of this relationship. The information provided above is just that, information, to be used as you see fit.