What happens if my grandmother owned a property but she died without a Will?

The timeline of who died when is not clear from your question: you may wish to re-post with additional detail. If your grandmother died without a will before your father did, her property was inherited in equal shares by all her then-surviving (alive at the time she died) children. So if she had four living sons when she died, each one got 1/4 of her estate under the rules for "intestate succession"--who gets what when someone dies without a will. Your father would have been a 1/4 owner of the home. When he later died leaving you his estate or his interest in the home, you became a 1/4 owner, together with his siblings (your aunts and uncles) or their own heirs. So you cannot by yourself make the decision as to what to do with the property but have to decide jointly with the other owners, or else bring a type of legal action traditionally called an action "for partition" to force the sale of the house and distribution of the proceeds therefrom to the owners.
If your father died before your grandmother, he did not inherit--only her surviving children inherited when she later died, and his share would gone to his siblings. Since he would not have inherited if she had no will but but died before  him, you did not inherit: you don't inherit from him, since he did not live to get his share, and a grandchild does not inherit when there is no will leaving something to him but there are surviving children.