[Drifter]

Off the top of my head, I can think of 4 traits that one set of wheels might have to increase efficiency over another set of wheels the exact same size.

1) Aerodynamics. At highway speeds this will be more important than the other three traits combined. Aero covers or more aero-shaped spokes will add weight but still increase efficiency.

2) Moment of inertia. This isn't just weight, but also where the weight is placed. Take two otherwise identical wheels. Put heavy lugnuts on one and lightweight lugnuts on the other. Put stick-on wheel weights on the rim to equalize the total weight of the wheels (i.e. offset the lightweight lugnuts with extra weight on the outer rim).
If you spin the wheel with the extra weight at the hub, it'll accelerate faster than the wheel with the extra weight at the rim because it has a higher moment of inertia. At steady speed the extra moment of interia will not matter at all. When you accelerate, it'll require a bit more force to overcome the momentum.
On the other hand, that extra momentum will help when you coast. So if you never used your brakes, the extra moment of inertia would not hurt you. If you do use your brakes, you're wasting that stored flywheel energy so you'd be better off not storing it in the first place.

3) Suspension losses. This one is almost always overlooked, so bear with me. We all probably remember Newton's law: Force = Mass × Acceleration. So any time a mass accelerates, a force has acted upon it. When you drive over a speedbump and the car bounces upward, the mass of your car has accelerated. A force was applied, and that force ultimately came from your tire & wheel.
A good suspension system will limit how much the main mass of your car moves and one of the primary factors in how nicely a car "rides" is the sprung to unsprung weight ratio. Sprung weight is the mass of your car, suspended on springs. The distance between sprung weight and the ground varies as the suspension absorbs bumps. Unsprung weight is the mass of everything that remains the same distance from the road over bumps. Tires, wheels, brakes, solid axles, etc.
A 2000lb Geo Metro with 40lb wheels at each corner will ride like crap. A 4000lb Cadillac with those same 40lb wheels will ride much better. Same goes for an unloaded pickup truck vs one with 2000 lbs in the bed...
If this is hard to conceptualize, take a road bike and air up the tires to 120psi. It'll roll great on smooth pavement, but you'll be jarred around if you ride on the rumble strips of a highway shoulder. Air those tires down to 75psi and you'll roll a little worse on smooth pavement, but a whole lot better over the rumble strips - you'll actually roll farther. That's because on the rumble strips the suspension losses on a 120psi tire are higher than the increased hysteresis from the 75psi tire flexing its sidewall more.

4) Hysteresis of the wheel itself. Hysteresis of the tire, as mentioned above, is the primary source of rolling resistance on smooth surfaces. The sidewall flexes and unflexes every revolution, creating heat which is energy that ultimately comes from your continued motion. If you flex a rubber band a bunch of times quickly you can feel it heat up.
Wheels also flex, just much, much less so. A stiffer wheel will roll better than a softer wheel. Steel is about 3x stiffer than aluminum, but the shape of the wheel probably matters even more. Steel wheels tend to be thin stamped assemblies while aluminum wheels tend to have thicker spokes/walls.
Again you'd be hard pressed to measure the difference in rolling resistance based on a wheels stiffness so you can just ignore it unless you're in some sort of super competitive event.