In order to use sterile water for something like a wound packing or cleaning, you'd also have to have a sterile field to do the dressing change with. You'd need sterile gloves, sterile gauze, sterile syringes, etc. If you had all of that, you likely had sterile saline to use as well. However, in a SHTF situation, you're probably going to aim for clean conditions vs. sterile conditions just b/c a sterile environment is going to be nearly impossible out in the field.
As far as drinking sterile water. I really don't see the point. As soon as it touches your lips, it's no longer sterile. Plus, your gut is one of the most bacteria laden environments there is. Adding sterile water to it won't change that.