**Key Question: Is this receptacle switched?
I hope the answer is yes. If it is not, then there is something strange going on.
Assuming it is switched - i.e., flip that switch on and the receptacle has power, off and no power:
- Hot flows through the box using the blacks
- Neutral flows through the box using the whites
- Switched Hot comes from the switch on the red wire
That is totally normal. But what is not normal:
- Duplex receptacles with only one screw on each side. That is technically OK but very unusual these days.
- No ground pin! That was quite common 50 years ago. You definitely want to fix that. If you were planning to replace with ungrounded receptacles, return them.
The good news is that you almost definitely have ground. You have metal boxes. The only question is whether you have ground wires connected to the metal boxes. You can poke around and look for them - should be a bare copper wire coming out from each cable. Or you can use a multimeter to check for very low resistance between neutral (white) and the metal box. Assuming the boxes are grounded:
- If you use a self-grounding receptacle, you just screw it in and done.
- If you use a non-self-grounding receptacle, you need to connect a ground wire from the ground screw on the receptacle to the metal box with an appropriate screw.
In addition to a multimeter, I recommend a "Magic 8-ball" tester:
These don't give definitive answers to strange wiring problems. But for standard receptacle testing they work quite well, and are a good way to double-check your work when you think you are done installing a receptacle. If you see anything other than "CORRECT" then you know something is wrong (even if you may not know exactly what is wrong).