I think those are equal in degree. They all express a very high degree of 'bad'. In short, there's no difference.

You could use any of them, although the meaning is not exactly the same. 'Awful' and 'terrible' are similar in meaning, equating (more or less) to 'really bad' and 'extremely bad'. 'Horrible' is slightly different, as this is closer to 'extremely unpleasant'. Whereas bad, awful and terrible are value judgements, 'horrible' is more personal, as it provokes a physical or emotional reaction.