You may not like this answer, but what you are describing your ex doing is a crime. It's called identity theft.
You really have two paths here. One, if you're on speaking terms, confront your ex, and insist that she pay off the debt as soon as possible (and I hope you've cancelled the credit cards, in the meantime). If she does that, it hurts your credit score, but at least you have your money back, and it may be the way to go if you don't want to take the second route.
The second route is you go to the police or, better yet, get a lawyer, who will likely suggest you sue her in court. (I'm assuming that you're a stand-up guy, and that this isn't a case where she's caring for your kids, and you're thousands of dollars behind on child support, and she decided that this was the only way she could get money from you. Still, even if that were the case, it doesn't change the fact that her alleged actions are illegal.)
As for getting those credit card accounts off of your report, you'll have to contact the three credit bureaus, Equifax, Experian and TransUnion. If you can prove that your ex-wife opened these accounts without your knowledge, they'll remove the accounts. Proof, of course, might be difficult to establish. But if you take your wife to court and the judge rules in your favor, you can send your court documents to the three credit bureaus with a letter explaining what happened, and I suspect that within a few months, those credit cards will be off your report.
And, of course, this doesn't address the fact that if you or your ex-wife are not at least making the minimum payments on these credit cards, your credit score is going to start plummeting -- and it's probably gone down already since you're carrying more debt and have more credit lines open than you once did. So I would get this fixed and fast.
No matter what you do -- try to collect from her, take her to court, or do nothing and hope for the best, you're in for a long slog, and I don't envy you. Good luck with whatever you decide.