"Although the L1, L2, and L3 points are nominally unstable, it turns out that it is possible to find (unstable) periodic orbits around these points, at least in the restricted three-body problem. These periodic orbits, referred to as "halo" orbits, do not exist in a full n-body dynamical system such as the Solar System. However, quasi-periodic (i.e. bounded but not precisely repeating) orbits following Lissajous-curve trajectories do exist in the n-body system. These quasi-periodic Lissajous orbits are what most of Lagrangian-point missions to date have used. Although they are not perfectly stable, a relatively modest effort at station keeping can allow a spacecraft to stay in a desired Lissajous orbit for an extended period of time. It also turns out that, at least in the case of Sun–Earth-L1 missions, it is actually preferable to place the spacecraft in a large-amplitude (100,000–200,000 km or 62,000–124,000 mi) Lissajous orbit, instead of having it sit at the Lagrangian point, because this keeps the spacecraft off the direct line between Sun and Earth, thereby reducing the impact of solar interference on Earth–spacecraft communications. Similarly, a large-amplitude Lissajous orbit around L2 can keep a probe out of Earth's shadow and therefore ensures a better illumination of its solar panels."

Earth-Sun L4 and L5 is more stable, but almost useless as a waypoint; however there are already naturally captured asteroids (and a lot of dust) already there.

All orbits require station keeping in a dynamic solar system that is circling around a black hole.

I am totally with you on using the asteroids for materials, but I am not sure that they would provide useful gravity either. Even one of the largest near-earth asteroids, 433 Eros, only has a surface gravity of 0.0059 m/s^2. Is that useful?

I mean that the habitable modules would be located inside silos embedded within the asteroid, so that the living space would be entirely surrounded by radiation shielding mass.

That would be pretty dark and cold.

The problem in space is generally getting rid of heat. Vacuum is a great insulator, insulation material is effective and relatively cheap, and radiative cooling is fairly slow. The other thermal problem is exposure to direct sunlight. The asteroid as a shell of massive shielding would help in this regard.

With enough time, and high enough specific impulse/in place fuel extraction, you can move anything.

The size of asteroid we are talking about here is likely to be closer to a container ship or maybe a small hill. Perhaps 1 millionth of the size/mass of Ceres at the most.

This could be an interesting new step in human modification of the environment - "orbitforming" (like terraforming?) a better solar system. It's like razing a hill to make way for farmland or better city building conditions.

An asteroid that's easy for vacationing billionaires, mining companies, and highly-pollutant industry to reach would be a great next step for humankind.

The L2 Lagrange point is "behind" the moon.