Compatibility summary
You will need a travel adapter in Oman; plug types used there differ from South Africa.
Plug comparison
South Africa plug types: C D M N
Oman plug types: G
There is no common plug type between South Africa (C D M N) and Oman (G). You need a travel adapter.
Voltage comparison
South Africa: 230V, 50Hz
Oman: 230V, 50Hz
Voltage difference is within a range many devices tolerate; check your appliance label.