Yes. He used the energy, water, garbage etc. Small claims court is ready-made for your situation.
Sorry that he is not taking responsibility for his 'bills'. Could be one reason he is now an 'ex'.
This is general legal information, not intended to apply to your specific case. And I may not be licensed to practice in your particular state. Under Federal Law, I am a debt relief agent.
Yes, if you pay these bills you should be able to recover the money from your ex-spouse. Ideally this issue would have been addressed in your divorce judgment; you should review the judgment to see if there are any relevant provisions. I don't see a way that you could recover for injury to your credit, etc.
You can sue your ex-husband, but you will still be responsible for those bills since your name is on them. Remember you signed an agreement with the utilities to pay for services. The utility doesn't care who actually uses them but who's name is on the account.
I practice Bankruptcy in Texas so my point of view is biased towards Texas law. This is not legal advice and does not establish a attorney-client relationship.