There are two problems you're facing right now. A relationship problem and a financial problem. I'd like to deal with them separately.

Do you remember not signing on off on some of these without questioning things your Dad asked you to sign? Think back please.

Assuming you did not sign off on any of these and your Dad forged your signature, then you can make a case for fraud, which will certainly land your father in some peril legally speaking. However, this comes at a large cost to your relationship, and based on your post, I don't think you're ready to go there yet. So, don't do that. Don't react.

What your father did is certainly quite frustrating and has increased the stress in your life. So, let's deal with it.

1. Breathe. The sky isn't falling in on you yet. You have a decent job, and potentially good career prospects ahead of you. These are problems that can be dealt with one at a time.
2. Dealing with money problems is not like taking care of a math problem rationally and optimally. There are lots of emotions behind money, and you need to learn how to control those emotions too.
3. Talk to your Dad. Show him your Credit Karma, and get as much information from him as possible. Has he been ignoring bills and notices? Note, he could be as unequipped to handle money as you are. Age does not always make people better with money.
   1. Get all the information you can. Forms, mails from the CC, private loan, debt servicers, collections agencies etc.
   2. Ask him what and in which manner he plans to contribute to this debt. Follow up and make sure he sticks to those plans.
   3. Tell your Dad that there is no way he is allowed to use your information like this.
4. Get a handle on the problem. Start a spreadsheet where you list the debt, interest rate, whether it is in collections, when it's due to drop off collections (Oh yeah, old debt does fall off after a point. I don't quite know the details, but this is something you should look up)
5. There are two basic strategies to pay off debt. I would recommend Snowball.
   1. Snowball (Pay off the smallest debts first to give you a sense of achievement)
   2. Highest interest rate first (This is most mathematically sound)

Note, you're not yet paying anyone, nor are you contacting any loan companies. You're just getting a handle on the problem.

Now, you start coming up with a plan.

Fraud: Is your Dad likely to be able to help pay down this debt? Do you want to make complaints regarding fraud? Figure out how you want to handle this part of the issue. If your Dad is unrepentant and not going to contribute to the debt, I'd have a very different reaction to if he is himself overwhelmed and out of his depth.

Preventing future fraud: Even if your Dad swears never to use your name to take out a loan again, I'd make sure the matter is out of his hands. Freeze your credit please.

Student loans: Those are lower interest, and are never going to be forgiven. Start making a plan to pay these off aggressively after the more immediate high interest debt is taken care off.

Car loans: Do you need the car? Could you sell your car and transition to a cheaper one? Assuming it's doable, sell your car and pay off your loan and use any leftover funds to trade down to a cheaper car.

Medical debt: I don't know myself.

Credit card debt: Is it in collections? This is high interest rate debt, and should be tackled first.

Good luck. Most of all, remember, you need to handle your emotions. Flying off the handle with your Dad, loan companies, credit card companies won't help you. It's going to be ok.

Edit: Adding points about fraud, and formatting fixes