Exactly which phone and Android version are you running? I ask because if it's a recent model, it would be very difficult to do anything to your phone via WiFi without you knowing it. It is more likely that they have somehow hacked your gmail account and are pushing apps from the play store that might give them some level of remote access.
Let's talk about security here.
Wifi. Make sure you are using WPA and you do NOT have any guest access enabled. You should also enable MAC filtering and ONLY permit access to your personal devices and deny all others. That will keep them out of your Wireless network.
Speaking of networks, do you have any wired connections? As a matter of fact, it might be helpful if you give us a list of all devices that connect to your network including any IoT appliances like cameras or smart thermostats. Do you have any roommates? Spouse? Children? Tenants? etc. who use your network? We really need to look at all vectors for intrusion if this is ongoing.
It's quite possible that if they could have hacked your phone, they could have also hacked your PC/laptop and installed a keylogger, so every time you change your password, they know the new one. You can easily check this out by going to a different network, use a different PC and change it and then, for a week or so, don't login using any of your devices other than your phone. If the shenanigans stop, then you can be pretty sure they have access to other devices as well, at which point I would consider either taking them to a security professional for evaluation or backing up your data and completely wiping them (start with a new hard disk and reinstall everything from scratch). And, when you do that do not NOT NOT NOT ever make your main account an administrator.
Finally, if you are dead sure they are accessing your communication devices and altering them, then give you local FBI office a call and ask what your options are. That is, after all, a federal crime. Hard to prove if they are, and possibly they are just screwing with you by being a bit more tech savvy and taking credit for things they aren't responsible for but know will happen.
FWIW, I have some whack-job neighbors, too and the only thing that works for me is to completely ignore them. As long as they think they are getting to you, they will most likely keep it up.
