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 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.
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.
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.