My father was born in Norway and moved to the USA with his parents when he was 4 years old (1914). He has since passed away. I wonder if there is anyway for me to obtain dual citizenship with Noway and the USA.
No. Norway does not allow dual citizenship. If your father never naturalized, and never served military service and never applied for american citizenship, then you may have had a claim on norwegian citizenship at birth. But that would be forfeited with any activity on your side to achieve american citizenship, or serving of military service.
The law has been tightened over the last 10 years to the point that dual citizenship is not almost impossible. But since every other country in Europe is loosening on this and allowing dual citizenships, I believe we'll follow suit within the next decade.
You would have to intend to live here though. Citizenships would not be handed out to people who do not intend to live in norway.