what your describing isnt someone logged on to your network, what you need to do is (a) rename your network from default (b) turn on WEP and (c) hide your SSID, also changet your defautl password since all linksys routers are IP 192.168.2.1 user name [blank] password "administrator", also Im assuming your using XP, if so go into the wireless settings and specify the network, and only that network, dont list ANY or no SSID, and with WEP enabeled it will help.

Tom wha tI think keeps going on with yours is your DHCP tables are messed up and when your ISP givs you a new IP its not updating it automatically