Compatibility summary
You will need a travel adapter in Oman; plug types used there differ from Japan. Voltage differs by more than 20% — a voltage converter may be needed for some appliances.
Plug comparison
Japan plug types: A B
Oman plug types: G
There is no common plug type between Japan (A B) and Oman (G). You need a travel adapter.
Voltage comparison
Japan: 100V, 50Hz
Oman: 230V, 50Hz
Voltage converter recommended (Japan 100V vs Oman 230V).