What makes radio waves refract? What materials cause radio waves to refract? What are the radio IOR's of these materials?
 A: Radio waves refract – they effectively bend in the atmosphere – and it is the ionosphere e.g. 60 km above the surface where they do so. See e.g.

http://www.tpub.com/neets/book10/40e.htm

You may imagine the atmosphere to be composed of many horizontal layers with different values of $n$ and the refraction satisfies Snell's law.
A: All materials with a dielectric constant different from vacuum or air will refract radio waves.  I could ask just what range of frequencies you want to know about, since "radio" covers a very wide span, but it doesn't really matter.  
Interesting things can happen at higher frequencies, like infrared and certain at optical, for most materials, but at radio it's a matter of dielectric constants and boundary conditions.  We're often dealing with objects, parts, obstacles of the same order of magnitude as wavelengths, where ray optics is not a good approximation.  
Absorption is also significant.  At optical frequencies, glass is transparent because the molecules have no quantum states with the right spacing to absorb visible-frequency photons passing through. (This is for clear glass, of course - colored glass is a different story.)  If you had something like a huge chunk of cardboard, say a cube mile on each side, and measured how it affected AM broadcast radio, or Bluetooth signals, there are all kinds of molecular vibrations, rotations, and collective motions that are happy to absorb small amounts of energy.  Metals, ionic fluids, and easily polarizable substances will happily eat photons, so it's not meaningful to speak of refraction - not enough comes out the other side to let us say anything has been refracted.  
In electronics engineering, we often combine refractive phase-shift effects with exponential decay with depth through a substance in a complex-valued dielectric constant.  With some math gymnastics, engineers define a "loss tangent".  The index of refraction is related to the dielectric constant  as $n^2 = e$ (n is IOR, e is dielectric constant).
There a many places on the web listing dielectric constants and related quantities.  This one seems good for a gaze upon:  http://www.rfcafe.com/references/electrical/dielectric-constants-strengths.htm  with several common substances listed.  Bottom line: just about every substance refracts radio waves.
