Appreciate all the information. The only thing that's missing is the credit limits for all the cards you listed. That would allow us to determine what your utilization is an each card and in aggregate.
Either way you should consider the avalanche paydown method, or the snowball method.
Avalanche is going to the best for you financially, saving you the most money in interest. You'd start with the highest balance, highest interest rate revolving credit card you have and throw every extra dollar you can at it until it's paid in full while making the minimum monthly payment on all your other accounts. Once that's paid off, you move to the next highest and so on. As you pay these high balances cards off you'll accumulate more extra funds to throw at the next one.
Snowball is the opposite of avalanche where you'd start with the lowest balance cards and as they're paid off you put the extra money towards the next card until they're all paid.
As your balances come down and your scores go up and that will allow you to start looking at refinancing the higher interest loans.
Some other notes. Getting the medical collection to below $500 will get it removed from your reports. If you have lates due to come off the first of the year, you're likely already eligible for EE (early exclusion) from TU. They'll remove adverse information 6 months early. EX will do 3 months early. EQ 30 days early
