I'm sorry, but after trolling a bit here, I had to put in my 2 cents.
To me, it seems like something straight out of a horror movie. I know, for a fact, that being able to monitor and control other people's computers is possible, but for someone to hack a phone (specifically an Android), that would require more than just a key logger. To me, it seems like you were browsing the internet via your PC on your neighbors' WiFi. If he was at all tech-savvy, he could have easily gained access to your PC and changed some things around. Being as it may, if the hacker was able to, in any way, gain your GMail account and password information (which is very easy to do if the victim does not have any sort of firewall or anti-virus installed on their PC) and logged in to the Android market and force-fed your phone apps that were potentially hazardous to your phone.
Again, this is just what I figured from what's been said thus far.
In any case, I would recommend doing what many here have said before. Turn off ALL (and I mean ALL) data connections on your PC, Phone, and any other internet-related device. If you have to, rip the cords out from the wall.
Wipe all the data on your hard drives (back up important documents to an external or flash driver) and start over from scratch.
Before even THINKING about connected to the internet, purchase a well-known anti-virus program like Norton and make sure it is up and running. Then, connect back to the internet and just keep an eye out for any suspicious activity that Norton records.
Lastly, make sure your personal ethernet router has at LEAST a WEP key. If it does not, call your service provider and tell them to set one up for you. Then, reconnect your other internet-related devices and start over. Again, keep an eye out for suspicious activity.
Record anything that happens that seems abnormal. Take your proof (records) to the police and ask them what you can do to stop the intruder.
Best of luck to you, mate.