If they're no longer necessary, it's always a good idea to cancel the cards. It doesn't help or solve the problem, but it does reduce risk and prevent future use.

As far as solving the problem, there are two solutions. Paying it or filing for bankruptcy. Under the paying it option, there's two paths: paying it all over time (downside: takes time, costs more) or paying a portion as a settlement (downside: get a 1099c for the difference).