Tires

River wear (sometimes called "errosion" wear is when there tends to be faster wear on the edges of each rib than in the center of each rib. It is, unfortunately, a common wear condition of tires that are on vehicles with excellent alignment and in a type of service that provides little scrubbing (long distances on Interstate highways, for example). The same vehicles in a high scrub application will tend wear faster and the river wear tends not to occur. So, as odd as this may sound, river wear is actually a good thing...alignment is good and the wear rate is slow.

If the tires on a vehicle have developed a flat spot due to being parked for a very long time, I know of no way to remedy the situation if getting the tires warmed up with an extended drive doesn't work. Most people who store vehicles (RV's, classic vehicles, etc.) drive them ocasionally just to keep from flat spotting tires. The casing and belts of the tires can be come distorted due to a lack of rotation. If the flat spot is due parking for a short time period, it typically goes away within a few miles of on-the-road driving.

All other things being equal, wider tires are less fuel efficient that narrow tires and smaller diameter tires are less fuel efficient tires than larger diameter tires.

Without seeing or driving the truck, I would be inclined to think that your problem is not tire or wheel related if the shimmy and shake only happens with the truck is loaded. Since you are not feeling anything in the steering wheel, it is pretty obvious that the problem is somewhere in the rear of the vehicle. Loading the vehicle would change the angle of the driveline. I wonder if there is a problem there?

Having different tread patterns across the drive axles(s) of an over the road tractor is not a problem (and not against the law, to my knowledge). The concern is the potential for duel tires having different diameters due to different tread patterns (or different tire brands) or different states-of-wear (a worn out tire next to a new tire). We recommend that dual tires have diameter differances of 1/4 inch or less. The larger of the two tires will carry most of the load. This can cause both tires to wear irregularly and potentially create an overload situation on the larger tire.