The following is
not guaranteed to be the cause of the problem. By reading the next paragraph, you
implicitly agree not to sue me if you buy a new router and it doesn't solve the problem.
What brand and model of router? If it's a non-Apple router and supports WPS (WiFI Protected Setup), you need to disable WPS in the router's settings. If it supports WPS and doesn't have an option to disable WPS, you need to consider replacing it (check for a firmware update first which might add an option to disable WPS). WPS is broken and allows anyone to use your wireless network regardless of your password strength (it's way easier to figure out the WPS "password" than it's supposed to be).
If you have an Apple router, you are OK and there must be some other explanation.
There are other possible explanations (those may actually be computers on your network, etc.). I'm just suggesting one possibility.