You Do Need power plug adapter while traveling from Nauru to Vatican City.

Here is Why You Need An Adapter

The outlet and plug type used in Vatican City are C, F and L and in Nauru is I. This is how they look like.

Nauru

In Nauru, outlets of type I are in use.

Type I

Vatican City

In Vatican City, outlets of type C, F and L are in use.

Type C

Type F

Type L