You Do Need power plug adapter while traveling from Oman to South Africa.

Here is Why You Need An Adapter

The outlet and plug type used in South Africa are C, M and N and in Oman is G. This is how they look like.

Oman

In Oman, outlets of type G are in use.

Type G

South Africa

In South Africa, outlets of type C, M and N are in use.

Type C

Type M

Type N