Draw how you are going to run the conduit from point to point. We can help you with the wiring... Post the pictures and I can AutoCad the thing for you with wire counts per pipe. No way I can figure out what you are trying to do or counts in the pipe if I don't know the final piping scheme or intent of the owner
Gary has it right and this is a great offer. We can tell you how the wires hook up schematically, but if that doesn't tell you what wires you need in what conduit then we can't help without the actual conduit routing. Your fist post is not exactly right. Electrically you have to look at three way and four way switches separately.
3-way switches have power from the panel coming in one end, two wires between them we call travelers, and a switch leg coming out the other end. When you do a house in romex you usually do as you said, run 3 wire looped through. That third wire is not always the neutral though. It can be the hot, the neutral or the switch leg, depending on how you twist the wire nuts together and which end you feed the lights from.
4-way switches merely intercept the travelers so they require four wires to them 2 in and 2 out. But since, in a house you are "carrying" one of the above wires through, you run 3 wire each way.
In most conduit situations, you will have one conduit running to a four way that is "junctioned" So that conduit will only get the 4 wires and the ground as discussed.
Regarding you fundamental question of whether you have to run the neutral with the other conductors, the answer is more complicated than yes or no. The neutral has to share the path with the hot, and/or switch leg, but not when it is going to a control device. The intent of the code is that you don't have the hot traveling one way around the house and the neutral traveling another.
Hope this helps. Again, take Gary up on his suggestion.