How do I wire mutilple sections of lights with 3 way switches to same power source?
Your problem is that the run from the 3 switch box to the top of the stairs doesn't have enough conductors.  In addition to the hot and two switched you now have, you will need a neutral return for the new single pole section.

You could use conduit here, but there's no sense ripping out the 14/3 that's already installed.  Just run a 14/2 parallel to it as shown. 

I'm guessing about which switches must control which lights, but here is a suggested wiring diagram:



B = black, W = white, R = red, where indicated.  Wires not marked in the diagram are all switched, so use whatever conductors are available, and please mark the ends of them with a bit of yellow tape for future maintainers.  And don't forget to hook up the equipment grounding conductors!

I have omitted the details of the lights wiring as you have already done these.

Pay special attention to the connections in section 1 as the neutral wire here is carrying the load for the entire basement.

Late Edit: I just noticed that in an earlier diagram I recommended what is a code violation in most places. Justin W. has long since finished or abandoned this project, but I don't want to mislead anyone else who might read this later. 

I have modified the diagram to show which conductors should be parts of a cable, in order to satisfy modern code, balance the current flow in each cable, and avoid inductive heating, magnetic radiation, and excessive line losses.