Check your router manual, if your router has a logging feature it is for sure mentioned in the manual. In most cases such extensive logging is not enabled by default, only errors are logged. Don't even bother checking if someone has used your wireless router, because if you haven't had ESSID broadcast disabled and haven't used WLAN encryption, someone most likely has.
In any case, you should ALWAYS have WLAN encryption enabled, either WPA or WEP, of the two WPA is more secure. Secondly, you should ALWAYS have ESSID broadcast disabled. When ESSID is not broadcasted, you can wirelessly only connect to the router if you know its ESSID. In this regard it is a bad idea to use default ESSID. You can make your wireless router even more secure by using MAC filtering, check your router manual for details. In most cases using unique ESSID, disabling ESSID broadcast and setting up WPA encryption is enough.
Insecure wireless router is basically you screming to the neighbourhood "Free broadband right here!"
Edit:
Google is your friend