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

Here is Why You Need An Adapter

The outlet and plug type used in Oman is G and in Djibouti are C and E. This is how they look like.

Djibouti

In Djibouti, outlets of type C and E are in use.

Type C

Type E

Oman

In Oman, outlets of type G are in use.

Type G