My father and his adopted parents are all deceased; however, I have always wondered who are his biological relatives. Can I learn this information and where should I start?

Genealogical search...

Do you have the names of your biological grandparents?

If not, chances are that you will not be able to find records of your biological grandparents. Those records are sealed, and if everyone involved is deceased, there is no way to get permission to open those records.

If you do have some information about them, you can try hiring a licensed private investigator, but depending on how long ago it was, you may not be able to find any information--either because everyone involved is deceased, or because written records will be next to impossible to find. You do not mention the year your father was adopted, which could change my answer completely. Adoption searches change based on the year of the adoption, mainly because of how records were kept and whether those records were sealed.

If you have their names you can start at your local library archives of marriage, death certificates, and birth records. Or online through the state from which they lived.