running lites won't go off with the switch of on my 1995 Honda civic e

There are two ways to turn on running lights; headlight switch or ignition switch. With ignition off, disconnect battery negative, wait a few seconds then reconnect and check if running lights stay off. Followup troubleshooting depends on running lights remaining off. With ignition OFF, manually cycle the headlight switch several times to see if its the headlight switch causing this problem. If it binds then it may be worn out. With a worn ignition switch, you're only option would be replacing it. If your Honda uses a body control module(BCM), it may be faulty.