The thing that concerns me about your post the most is that you do not pay a mortgage payment yet you have 75% credit utilization on your credit cards. This means you spend more than you make and that right there is a problem. You make a substantial income so you should be able to do some work and get in a better place in a few simple steps. I have done this very same plan, so if you have any questions please let me know.
Step 1: cut up and stop using your credit cards.
Step 2: Save up an emergency fund of at a minimum of $1000. Do whatever you need to even if you have to sell things or whatever, but try to do this in 3 days if possible.
Step 3: Cut out any non-necessary expenses by creating a budget. Determine what your fixed expenses are and make sure you include your annual expenses as well. Then determine what your monthly variable expenses are. Once you know your required expenses that are necessary for the near term then you can evaluate your non essential expenditures. Do you buy coffee or go out to eat? Do you make purchases that you haven't planned a head of time. Do you have monthly subscriptions on things you don't need or use? Could you re-evaluate your cell phone plan, internet, television and lower the expenses or shut off temporarily? Could you rent your house and move to an apartment or with family? Do you have an extra room that you could rent? Find a away to understand what you spend your money on and how to free up some extra cash so that you can use it for the next step.
Step 4: By this time you should have freed up some funds that you can now start applying to your debt. I recommend starting with our highest interest rate debt but you could also work on paying off the lowest balance first. Take whatever money you have freed up in the previous step and put it towards paying down ONE of your debts. Don't spread it across several because you want to get one paid off as quickly as possible.
Step 5: Once you get one dept paid off roll that payment and the extra you were putting into it into your next debt. Keep doing this until your at a bare minimum your credit cards, are paid off. But preferably your cars and student loans are as well. Once you hit this point your credit score will increase. Do not close your credit cards after you have them paid off. . . trust me this was a mistake I made but do not use them for personal expenditures unless you have the self control to pay them off every month.
Step 6: Save up at least 10-15K for emergencies and other large purchases you make throughout the year to ensure that you do not need to use a credit card if something comes up. Any time you use the money out of this fund, make sure you have a plan to pay it back quickly.
Step 7: Now you have the credit score back, some reserve in the bank and your DTI ratio is in better shape, banks will probably be very likely to give you a cash out refinance on your primary residence to use for investments.
Step 8: Go forth and do good things in the world!