Wiring – Connect a lamp wire to one wire or three

First recommendation; put labels on stuff. Sorry, nobody needs a Monday Morning Quarterback.

Do you have a meter? I would try metering out which wire gets voltage with the lightswitch going on and off.

My guess, based on the two way switch, is that the three black wires are; Line ( from the breaker ), feed to the outlet, and feed to the switch. The two whites in the wirenut would be the Neutral to the breaker box, and the outlet. I am guessing that the single white wire is a carrier from the switch, or in your case, switches. With this premise in mind I would check the voltage with a meter on the single white against ground while blinking the switch. If the meter blinks with the switch, then put the fixture black onto this wire, and white with the wirenuted whites.

If this guess is wrong, I have more questions. Did / does the outlet loose power when the lightswitch is off? If yes, then it's probably wired with all blacks together and all whites together. But again, I'd check with a meter before closing in all the boxes.

good luck, let us know the outcome

First, you can only connect one wire to a screw. If you need to connect multiple, then you create a pigtail by cutting a short piece of wire and attaching one end to the screw, and the other end is connected to the other wires with a wire nut.

Second, you need to figure out which cable provides the power to the box. Most likely it is the cable without the red wire.

Once you know which cable provides the power, then any black or red wire you want powered all the time gets connected to this black wire with a wirenut. You should also pigtail this wire to one of the terminals on your switch. Any red or black wire that you want controlled by the switch should be connected to the other screw of the switch, with a pigtail if necessary.

In general, ceiling lights with black and red wires are wired so that the black wire is for a light and the red wire is for a ceiling fan. Similarly, the black wire to an outlet typically provides continuous power, while the red wire is connected to a switch. In either case, if the red wire is unused, then you should wirenut both ends.