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

Here is Why You Need An Adapter

The outlet and plug type used in Oman is G and in Swaziland is M. This is how they look like.

Swaziland

In Swaziland, outlets of type M are in use.

Type M

Oman

In Oman, outlets of type G are in use.

Type G