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

Here is Why You Need An Adapter

The outlet and plug type used in Nauru is I and in India are C, D and M. This is how they look like.

India

In India, outlets of type C, D and M are in use.

Type C

Type D

Type M

Nauru

In Nauru, outlets of type I are in use.

Type I