Photons interact with matter if the matter offers quantum transitions that match, or nearly match, the photon's energy in the inertial frame of the matter. Ordinary matter such as wood, stone, etc. offers several groups of possible quantum transitions.
- Rotation of molecules (if they are free to rotate, i.e., not condensed matter)
- Vibration of molecules - bending, quivering actions
- Electronic excitations
- Nuclear excitations (there being various kinds, ignored here for simplicity)
Microwaves have such low energy they can't do much, though they might excite some types of vibrations on larger floppier molecules - however, any type of molecule that could be described as "floppy" probably isn't good for construction materials. Rotational modes aren't possible in a strong material made of crosslinked polymers or silicates. So microwaves mostly fly right through.
Near-infrared and visible light can kick electrons into higher molecular orbitals. Even if the energies aren't a match, just close, there is interaction, as Heisenberg lets them cheat temporarily. Also, having more energy, visible light photons can stir up a greater variety of vibrational modes. There's nothing in common wall materials to prevent that, and in fact, the interaction with photons is so strong that the material, if not super-thin (microns), will be opaque. Of course, glass is an exception.
Gamma rays are of such high frequency, electrons (or ions, or polarized ends of molecules) can't keep up due to inertia - so no interaction, or only a little. At the right frequencies, gamma photons can interact with nuclei, but for a randomly chosen source of gammas, its photons are unlikely to match closely enough with any of the available nuclear excitations, and can't really do much at the molecular level - therefore, the material is almost transparent.
All this is so oversimplified...
The light from distant galaxies does undergo a frequency change. It is red shifted, and the amount of red shifting is used to work how fast the distant galaxy is receding and therefore how far away it is. However this is not a damping effect. The light red shifts because the spacetime in between us and the distant galaxy is expanding, so although the light's energy is conserved it is spread over a larger distance.
You ask why light isn't damped, but why should it be? Since energy is conserved the light wave can't lose energy unless there is some mechanism to carry the energy away. For a light wave travelling in vacuum there is simply no mechanism by which it can lose energy, so it doesn't.
In your last paragraph I think you're getting mixed up with a different effect. When a terrestrial radio station broadcasts it sends the radio waves out as a half sphere (the half above the ground). As you get further away from the transmitter the field strength of the radio waves decreases as the inverse square of the distance because the energy of the transmitted wave is spread over a larger area. However the total energy of the light wave is conserved. This obviously happens with distant galaxies as well because the more distant a galaxy is the fainter it appears. This isn't due to damping, it's just the inverse square law dependance of the field strength.
Best Answer
They are self propagating. An oscillation in the electric field results in an induced one in the magnetic field, and vice versa repeatedly. Thus, it propagates itself through space with these repeated inductions regardless of physical surroundings.
See http://www.physics.usyd.edu.au/teach_res/hsp/u7/t7_emr.htm.