Are there conventions on which side to travel on Victor airways - USA?
If you are flying IFR the FAA expects you to be on the centerline of the airway, as per the FAA's IFR flying manual 


  to operate an aircraft within controlled airspace under IFR, pilots
  must either fly along the centerline when on a Federal airway or...


I can't find any references in the Airplane Flying Handbook to airways at all and keep in mind under VFR "see and avoid" is paramount but centerline is generally accepted. If you are flying with any kind of an autopilot/GPS unit thats where its going to put you. 

Moving to your IFR example


  And worse, if he were IFR at 6000' and right on the radial, that's
  even closer.


500 is more than enough for the FAA's liking especially when one of those planes is flying under IFR. 


  Most airways are eight nautical miles (14 kilometers) wide, and the
  airway flight levels keep aircraft separated by at least 500 vertical
  feet from aircraft on the flight level above and below when operating
  under VFR.


The reality is there is often even more separation since under VFR you are required to stay 500 below the cloud bases which are not always at round numbers you may often end up at the next lowest VFR cruising altitude  

It is however, advised that if you are flying IFR but climbing on an airway in VFR conditions you execute gentle banks to look for traffic.