If your father did not leave a will and was unmarried at the time of his death, you and any siblings are what are called "the intestate heirs." This means that you and any sibling(s) will share in his estate.
You or one of your siblings will have to initiate a probate proceeding to be appointed adminstrator after which the bank will have to disclose your father's assets and give them to you in your capacity as administrator. This involves a probate proceeding.
The girl friend is living in the house because no one is telling her to move. If you are appointed administrator you will be able to evict her.
My law firm of Reed & Mansfield does probates. For uncontested probates we believe we are the high quality, low cost, discount probate law firm. Give me a call if you would like to discuss starting a probate.
I am in agreement with John Reed's assessment and would only ad that the longer you wait, the greater chance of the girlfiend destroying the house or property in the house. In addition, if there is a mortgage, you risk having the house foreclosed upon which would take money from the value of the inheritance.