Examples 1 and 2 sound fine to me, although for clarity's sake I would change their wording a little bit. Number 1 would then become, "His addiction today is so bad that he is unable to keep a steady relationship." Number 2 would then become, "Since then, his addiction has become so bad that he has been unable to keep a steady relationship."
Example 3 is a little confusing by its combining of the past and present. The sentence starts out by referring to a time in the past (which could have been a few weeks or a few years ago). The reader then expects the writer to provide an example from the past, indicating how bad the addiction has been (and not as it is now). Hence, a better wording would be, "His addiction has been so bad that he has been unable to keep a steady relationship." Another possibility is, "His addiction has been so bad that [at one point] he was unable to keep a steady relationship." (While still addicted today, he may nevertheless be able to keep a steady relationship.)
Examples 4 and 5 can be eliminated because the victim, I assume, is still addicted. The "had been" from each example makes it sound as if the addiction is a thing of the past, which it is not.
