I have looked and looked as well with LOTS of mixed info. Here's the story.
A. If you have EVER jailbroke before, and have stored your shsh (3.1.2 or earlier) on cydia then yes for both. (jb and unlock)
B. If you have a stock phone that has never been jailbroke then no luck for either. You are stuck.
I had a problem with my phone and apple swapped it. Then I went to restore my old contacts etc, not even paying attention, and boom. 3.1.3. Doh. Now I have to wait to be able to tether. Luckily, when I swapped mine out I got an old bootrom, although its of no help at this point.
Long story short.. Stock iPhone jailbreaking 3.1.3 for the 1st time ever. NO. Its not possible (or publicly released yet).