Are there conventions on which side to travel on Victor airways - USA? I'm a low-time VFR pilot (100hrs) in the United States. I have not yet started IFR training (other than XC time building).

I understand the purposes and reasons why the Victor airways exist. I also understand the Victor airway widths are 8 NM minimum but widen when the VORs are further than 51 NM apart.

I regularly try to follow the Victor airways and VFR altitudes on VFR Cross Country flights, and do file VFR flight plans and use flight following. This makes it easier for me to communicate my position and seems it would be safer than just flying direct.

Question:

Is there a convention for a side of the "road" you should travel on in the USA?

My guess would be if a convention exists, it would be you should always travel on the right; this puts the red lights of the left wings of crossing traffic together, enforcing / encouraging avoid to the right; both A/C would make turns to the right, further expanding the horizontal gap between them. Right of way to the right, avoid to the right.

Background:

On a recent XC from KIXD to KSGF, I was traveling east at 5500' MSL and was directly over the radial, according to my GPS and my ODI. A west-bound crossing plane on VFR was at 6500' MSL and about 1 NM to the south of the airway. We both were using flight following and were alerted and there were no issues. But it made me pause to think, should I really be centered right on the radial? What if he were as well? Then there would be 0' horizontal separation, only 1000' vertical. And worse, if he were IFR at 6000' and right on the radial, that's even closer.
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.