We have a Lennox gh6 120C Furnace, original to our house, installed in 1959. I have two issues. First - we have a switch on the side that also has outlets on it. We have never used it for this, but is it to just turn on the blower? This leads to my second issue. When that switch is off, the furnace does not turn on at all. When the switch is on, the blower kicks on and blows air constantly. Even when I turn up the thermostat, the heat will come on, but then when the heat turns off, the blower keeps running, blowing cool air, never turning off. Any suggestions?

Sounds like you have a fan and limit control that is causing a problem OR a stuck relay. OR someone wired the unit to have the blower run all the time.