There are enough resources in our solar system to sustain the lives of a few billion billion people. Put another way, humanity's population can increase a billion times, and not put strain on the solar system. By intelligently reallocating the resources found in asteroids, uninhabitable planets, and the celestial bodies found in the Oort Cloud, humanity can grow without limitations for many centuries. Assuming a relatively high population growth rate of 2% per year (population doubling roughly every 35 years), humanity will have over 800 years before we will have to look beyond our solar system.
Transforming the Asteroid Belt
As more and more materials are required to build colonies in orbit, on the moon, and on Mars, humanity will have no choice but to claim the Asteroid Belt. Utilizing similar structures and technologies used to construct Asgard, the asteroids selected for mining will eventually turn into comfortable habitats. As this network of habitats grows, the Asteroid Belt will be transformed into a band of life, circling the sun. Asteroid habitats will end up housing the majority of the human population within our solar system.
How Far Out Can We Go?
Solar energy will be the primary source of energy in Solaria. However, its uses has its limitations. As light moves further away from the sun its intensity decreases exponentially. Fortunately the Asteroid Belt is not too far away. If a solar energy collection device of a given size can provide sufficient energy for a single person in Asgard, the same devices scaled up 4x larger can do the same along the inner section of the Asteroid Belt. In the middle of the Asteroid belt a solar collection surface 9x larger will be needed, and at the outer edge, 16x larger will suffice.
Once beyond the Asteroid Belt, it is unlikely that solar collectors will be an effective means of power generation. Pending a revolutionary discovery in energy generation, we will have to rely on nuclear power--hopefully fusion--to maintain liveable habitats. It is likely that the only reason we will extend so far out into the solar system will be for mining resources or redirecting comets and asteroids. For these limited purposes the power of the atom will be well suited.
Utilizing the Sun
First proposed in the 1960's, a Dyson Sphere is a structure that encloses a star in such a way that its full energy output is utilized. Of course, trapping all of the sun's energy would be disastrous for the colonies on Earth, Mars, the Asteroid Belt, and pretty much anywhere else. By using a Dyson structure with a gap large enough to provide light for the ecliptical plane (which the majority of the solar bodies lie along), the majority of the sun's energy can be harnessed without compromising established colonies.
Building a Dyson Sphere will require material, and lots of it. The elements in highest demand for such a task will be the heavier elements, such as metals. Fortunately when the solar system was first formed, lighter compounds condensed in the outer regions while heavier elements condensed in the inner regions. The result is Mercury, a planet of remarkable density in close proximity to the Sun. Most, if not all of the Dyson Sphere can be constructed out of that single planet. Trading an uninhabitable planet for control of the sun's energy is a good deal.