What length header should I consider?
hard to say without knowing more about the floor plan. Maybe they're in a longer section of floor. Maybe there are plumbing fixtures that required a shift in layout. Who knows? 
It doesn't much matter whether you use one header or three, but you'll want trimmer studs supporting it or them between each pair of doors. Otherwise you'd need to size the header for the full span, and that would probably call for a LVL beam.