Most credit card companies won’t actually let you close out the card with a balance due. You can destroy your cards, though so that even with an open account you can’t use the card.

Keep one or two with the best interest rates, (pay these off last) for emergencies.

Pay off the maximum amount you can on the highest interest rate first, while paying minimums on the other cards. Once you’ve paid off the highest interest rate, go to the next highest rate and pay that one the same way (max that while paying minimums on the others.) Do that until you’ve paid them all off. Close the cards out as soon as you make the final payment until you’ve worked your way down to zero carried balance on the card(s) you are going to keep. Pay these off every month and only use them for things you can pay off at the end of the month except in an emergency.

Good luck. Resolving debt is a good New Year’s resolution.