I was replacing an outlet (see image) and noticed it was actually on two different circuit breakers. Is this normal? It has 3 black wires and 4 white wires with one ground. Why would it be hooked up in this fashion?

From the picture, it looks like the tab between the two halves of the receptacle has been removed. This usually indicates that this has been split, with half as a switched outlet (controlled by a wall switch elsewhere in the room) and the other half wired as an always-live outlet. This is fairly common in living rooms and sometimes bedrooms.

But there would normally be an equal number of white & black wires in the box -- the cables come with them in pairs. I don't understand why there would be an uneven number. Does this box have cables coming in, or is it metal or plastic conduit with individual wires inside that?

I looked a little closer at this outlet and found the other black wire tucked away in the back connected to a red wire. I cannot find a switch that would control the flow of electricity but this outlet is in the living room. The electrical box is metal and the incoming cables are sheathed in common white residential plastic cable.