My house has led lights that are dimly light when the switch is off. They light up fully when the switch is in the on position. when I measured the voltage at the light socket I got 40 volts when the switch was in the off position, the light in my laundry room reads 35 volts when the switch is in the off position, the light in the laundry room works when the switch is put in the on position. I think it's a back fed neutral. I have the lighted switches in my house, could that have anything to do with it. when the first light in the hallway to my basement is screwed out of the socket and the light in the laundry room is also screwed out of the socket the light in the kitchen which is not an LED, but one of those older spiral lights, flickers more. both the two lights that I screwed out are LEDs.
I'm assuming that your lighted switches are lit when the switch is off. These work by passing a low current through the load to provide power to the built-in light. With normal incandescent lights as load, the current is too low to make them glow. However, the LEDs take so little power, that this small current will light them.
If you want to use LEDs, you probably need to either replace the switches or have at least one incandescent bulb on the switched circuit.