Ok, worse case situation is that your dad goes first. You stand to loose everything with no valid will. Get one made asap and have him appoint a personal representative. They both need POA for medical decisions as well.
If your dad should die then your mother go into nursing care they can not approve her due to assets and all assets would have to be "spent down" before she could qualify for medicaid. If your father is deceased at that time then the house counts as a possible asset. They can come back after admitting her and claim the house if titled to her.
So your dad needs to go ahead and quit deed the home over to someone now. He needs to draw up the deed and clearly state that he and your mother have "life rights" to the home. So at the death of both the home then goes to you in full.
The catch is there is a 5 year look back period for transfer of assets. The home, the money, anything that is done has a 5 year look back. Your dad can gift small amounts of money for you to hold. 5k, 10k, but larger sums catch attention.
If all the property and assets are transferred in time then they can not take them. If not then your mother or dad must qualify on their income if both are living. In this case the home and one car and the spouses assets are protected. And the one parent would be approved or not approved on their income alone from SSA or other retirement.
This brochure will assist some. http://www.mffh.org/medicaidbasics.pdf
I suggest that you sit down and attempt to explain to your dad the ramifications of not doing an "estate plan". I susgest that you find a local chapter of Elderlaw and take him there for a meeting for free legal advice on such planning.
But your dad needs to plan things now. At a minimum the home should be taken out of both names and quit deeded and giving them life rights.
Please reply if needed as I have typed this fast. If confused and need more info then let me know as i will be more then glad to continue.