3 way circuit with voltage in the off position
This sounds like capacitive coupling, straight-up

Any pair of plates or wires next to each other will have a parasitic capacitance between them.  For a typical length of 14 AWG NM cable between two switches, we're talking about roughly 75pF to the meter between adjacent wires, such as the two travelers in a three-way switch.

As a result of this capacitance and the fact that mains electricity uses AC not DC, a tiny amount of current can flow through a three-way switch setup when the switches are configured to turn the load off.  For say a 10m cable length (750pF of capacitance) on 60Hz mains, we get an inter-traveler impedance of 3.5M&ohm; and an allowable current flow of 34&micro;A with the load shorted.

This is an insignificant amount of current if you're an incandescent lightbulb; however, LEDs themselves require much less current to run, and the driver circuit in your LED fixtures is clearly finding enough power there to sustain operation at a low level.  (Some drivers have far larger capacitors in them, so they charge up, try to start up, drain out the large capacitor, shut down again, and then start charging again, resulting in flickering behavior instead of the dim glow you see.)

The 23V reading is similar -- a typical modern voltmeter has a very high input impedance (on the order of 10M&ohm;), and is going to read the parasitic voltage that was coupled across as a result.  (If your meter has a LoZ function, switching to that will cause the parasitic, or "ghost", voltage to go away.)