Can I sue a neighbor for giving my wife and I misery of loud noise for 3 years now?

Yes, you can seek damages for a nuisance in small claims court. Before doing so, you should have copies of letters you sent the neighbor asking them to reduce the noise level.

Loud is subjective. An injunction may be available if the noise rises to the level of a nuisance; this is probably not the case. The only other possible remedy is calling the police for disturbing the peace. Whether this remedy is available is also fact specific.

You might be able to file a nuisance action asking for an injunction.