Indians living in Oman may not be eligible for an Aadhaar Card.
However, they could apply for one if they meet certain criteria.
"Aadhaar Card enrollment is presently available to residents in India. Overseas Citizen of India (OCI) card holders who stay in India for a long time and have an Indian address can also enroll for Adhaar Card in India”- Indian Embassy
Indians living in Oman don't have to link Adhaar Card to PAN or don't have to quote Adhaar Card number in the PAN card.