Remove and Cap Light Switch Wires
It looks to me like the switch on the right is a former 3-way.  The black and red labeled "no voltage" were the messengers, and the black labeled "voltage" was (is) the supply.  

But we're not sure about the messengers or what they connect to.  If you can find the other end of the messengers, and establish that they are messengers, I would wrap yellow tape around all 4 wires (2 wires x 2 ends) to mark them as messengers.  They sell 5-packs of colored electrical tape for a few bucks. Don't mark them unless you can mark both ends, or you'll just make yourself confused later. 

It looks like they did the trick of baring a part of the wire 6" before the end of the wire, connecting it to a screw on switch 1 (right) and then continuing it to switch 2 (left).  That will be a little hard to put on a wire-nut unless you cut it in the middle of the stripped area.  Which would be fine.  

The other non-ground wires need to be capped, period.  You have no idea what they go to, and when you crunch everything back into the box, you don't want them touching a hot and "lighting something up" in the bad way. 

Are you sure a switch out there somewhere hasn't lost power?  There must surely be a partner 3-way to this one.  If you now find a switch in your house doesn't work, take it apart and see if it is the partner 3-way to this one.  If so, mark the messengers (disregard position, messengers are the brass screws), then at this end, connect one messenger to supply and leave the other messenger capped.  At that point the other switch will operate in one position or the other.  If it lights in the "down" position and you find that annoying, come back here and switch messengers. 

Lastly I see the screws are all the way out on your remaining switch.  That, and the hack-scratches on the loose wires, makes it look  like the installer used the "back-stab" wiring method.  That is a cheap builder trick to make wiring faster, but experience shows it is unreliable in the long term.  I recommend converting to either side-screws or go out and get the nicer Leviton "screw-and-clamp" type receptacles.