Sorry for your trouble. It would depend on the type and age of the taxes in question, as to whether they could be discharged. You likely qualify for bankruptcy and it could be a good idea, but to get more specific information, I would seek out a free consultation with an attorney in your area.
Yes, generally speaking state income taxes can be discharged in bankruptcy if they are over 3 years old, you filed the taxes more than 2 years ago, and they were assessed more than 240 days ago.
Without bankruptcy, I don't know how you would "dissolve" your state income taxes unless you could work out a settlement with them. You may need to hire an attorney in that state to do that. Otherwise, there is a statute of limitations on the collection of state income taxes in most states, again, it varies by state from 6 years to 20 years.
Medical debts do not usually sue you, if they do you could consider settling with them, fighting the suit, or filing bankruptcy. If 3rd party debt collectors are calling you and that is what is bothering you, you can send them a cease contact letter and they are no longer allowed to contact you about the debt (well, they will likely then send it to a different debt collector, and you have to send them a cease letter, and so on).
You really need a consultation with a bankruptcy or debt collection defense lawyer to look at exactly what your situation is, to give you solid advice.
We are a debt relief agency and we help people file for relief under the bankruptcy laws.
Please clarify. You say this is IRS debt, but from a state you used to live in. If it is IRS debt, it can definitely be dealt with due to financial hardship and lack of assets, even if it isn't three years old. And Offer in Compromise might be a good option if you still have tax debt left after a bankruptcy.