At this point, somebody needs to take charge and change the locks, secure the property, identify the assets and liabilities, and prevent foreclosure of the house or repossession of the cars. That person should likely be the person named as personal representative (a.k.a. executor or executrix) of the estate(s) under the will(s) and who likely had power of attorney before their deaths.
Their property might be “in limbo” until someone steps up to probate the will(s) or serve as administrator of the estate(s). Just because your parents verbally put you in charge does not mean that you have lawful authority to do whatever you want or need to do. Real estate, for instance, cannot be transferred by you without express authority of the court called “letters testamentary” or “letters of administration.” If there are debts, the estate’s property should not be distributed to the heirs until all debts are paid. Debtors can come after the personal representative and sometimes the heirs if property disappears.
So you may need to open an estate in the probate court for at least one of your parents. If there is a will, then a personal representative would have been appointed. You should file the will with the probate court, and in most cases the court will order the will probated and grant “letters testamentary” to the appointed personal representative. If there is no will, then someone would need to ask the court for an administrator of the estate. The administrator would pay the debts and distribute the remaining property, if any, to the rightful heirs under supervision of the court. You can petition to have yourself appointed as administrator.
Every estate has a different set of complications, so you should ask an attorney you trust for a short consultation just so you can get a view of the probate landscape. In most cases, a good attorney can coach you so you can take care of the estate. You want to avoid an error that might be hard to undo.