People think that because emails are sent with their name and email address in the 'From' box that they've been 'hacked'. It's rarely true. Malware - and real people, but it's usually malware - can use any address to disguise the origin of spam and they just use one off the infected computer. If that's the case there is nothing much you can do to stop it. Scan your own computer to ensure your own machine is not infected.

This sounds a bit different - the emails pretend to be 'next door' messages, IIUC. Somebody must run that - complain to them.

People who hack email accounts usually set up some sort of scam: Help! I've had my passport stolen. Send money! They usually set your account to automatically redirect your mail so they can intercept all replies, so that's the first thing to look for. (Which is hard because most people don't know you can do that.)