wireless network control issue

My Nintendo WII uses my internet wirelessly off of a router on a main computer (MAC). We recently , my wife and I, decided to let some neighbors who live below us to run their internet off of ours wirelessly as well and get some extra money of course. Anyhow, The problem is that every now and then I find that the WII comes online even when we have the power off to it when I observe the wireless network. My question is, is this because someone is trying to access my WII or turn it on wirelessly and if so, can they access other computers, namely the MAC attached to the router, and how can I make sure that other computers and electronics running off of the wireless feed from my router can't be accessed without permission and still allow other users to use the internet wirelessly?

Sorry for the length of the question.

 

Have you set up a secure wireless connection? Give the neighbors the network key and set up MAC filtering also.