I'm with Remedios, don't use your savings, keep growing that. Take any extra you have from any overtime and snowball the cards. Start with the ones that are still open and maxed out first. Don't use them if possible and just get the balances down. Once that is there tackle the car and finally the closed accounts. It will start to go faster once you get a few of these knocked out which may not take long if you can grab a little extra money from overtime or a side gig.
You may want to also take part of the snowball funds and add to savings until you can get a few months salary built up in it. That will give you a cushion and keep you out of this situation in the future.
This is a really good thread which may apply here
I second the DO NOT BE SHY/EMBARRASSED I started when I was a early 29 XD It's NEVER to late to get your life together NEVER!!! I would rid yourself of the collections when you can that will help boost your score as well but then work on a balance for the rest I have it set up so one of my cards is due the beginning of the month one in the middle and one at the end so if a hard time did ever hit I can rely on one of the later ones to help me out but don't make that your only and ultimate plan the plan is to be comfortable and only using as little as possible of your credit unless it's a die hard have to type situation. Once you lower your utilization and get the collections off you will see a LARGE jump or should at least! That is from personal experience 
Also plan out what cards work best for you and build on that one to help if you are ever stuck in the future too. People don't NEED more than 3 good cards so more doesn't always equal better! Good luck and keep us posted!
Here's the big thing, and I know I sound like a broken record because I always tell everyone this, is you MUST have a written budget where you can track all of your spending, down to the penny! Right now as you are getting on track it's important that you start to build a solid foundation that starts with sound financial discipline. Before I started to make a budget, I was always winding up with more month than money, robbing Peter to pay Paul, & never a steady cash flow. Once I wrote down ALL my expenses & what I was spending my paycheck on I was able to get a grip on my finances & start attacking my debt. I took all my monthly obligations, such as rent, utilities, car payment, phone, insurance, etc and allocated half of each amount every paycheck (every two weeks). By doing this I knew how much I actually had left over in cash flow to last me till next paycheck. This also steadied out my cash flow so I knew how much I was going to have every pay period. I found this method much easier than having a lot of cash flow one paycheck, then being broke the following when I had to pay everything.
You want to see where your money is going & identify your spending habits. From there, you'll be able to trim unnecessary spending & create cash flow, which will help you pay off your debt. You also want to continue saving part of your paycheck EVERY TIME you get paid.
Learn & understand that credit cards should not be used to buy things that you don't have the money for yet- that is how people get in debt. Use your credit cards as a convenient alternative to carrying cash with you, & pay them off every month, using the AZEO method. It will take some getting used to, but once you have your finances under control you will be amazed at how much more money you actually have!
Your budget should look something like this:
