While the actual efficiency of this strategy is questionable and involves biomechanics, friction, and many other complicating factors, the most reduced model can indeed be compared to the Oberth effect.
What you are "feeling" is the force you are applying. "Hard" is when it takes you a lot of force to move the pedals, "easy" is when it doesn't. Your body can be approximated to being capable of applying a certain force, and when it's "easy" to pedal, you can just pedal harder in order to reach your standard level of force.
In this view, you're no different from a rocket engine, which also applies a certain force to the spacecraft.
The Oberth effect, in its core, is about applying a force in the same direction as you are travelling, at the highest possible velocity to maximise energy the energy gain.
In the same way, the bottom of the hill is where your velocity is the highest, and an applied force would add the most energy.
This isn't necessarily a useful observation, since the forces slowing you down are also bleeding away a larger amount of energy at higher speeds.
Is biking up and down a series of hills a good real-world analogy for understanding either the Oberth effect and/or gravity drag?
I don't think so. If you understand the Oberth effect, you could point out the similarity. But you are in effect explaining a simple scenario with a more complicated one. "gravity", as explained by "biomechanics", "friction" and "gravity".
Analogies are useful when they can replace a difficult idea with an easier idea.