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

Here is Why You Need An Adapter

The outlet and plug type used in Faroe Islands are C, E, F and K and in Oman is G. This is how they look like.

Oman

In Oman, outlets of type G are in use.

Type G

Faroe Islands

In Faroe Islands, outlets of type C, E, F and K are in use.

Type C

Type E

Type F

Type K