I am wiring lights: line->3 way switch->4 way-> 3 way->load->Load->load->load->load. Can I run 14/2 Romex between loads, or should it be 14/3?

That's fine, unless at the other end you want to add a receptacle, then use 14-3, doesn't get easier or cheaper to run than now, if just the lights/loads, then 14-2..