Timatic (one of the database used by airlines to check what documents are required) says:
Visa
Visa required.
Visa Exemptions:
Accompanying spouse and children of a national of Bahrain, Qatar or United Arab Emirates for a maximum stay of 14 days.
TWOV (Transit Without Visa):
Passengers with a confirmed onward ticket for a flight to a third country within 24 hours. The connecting flight must be booked on the same ticket. They must stay in the international transit area of the airport and have documents required for the next destination.
Additional Information:
Passengers in transit with a pre-arranged Stopover Paid by Carrier (STPC) and a passport valid for a minimum of 3 months are permitted to leave the airport.
So in your case, as long as all flights are on the same ticket (and you can thus stay airside, no need to collect bags, check-in, or go through passport control for any other reason), you do not need a visa for Oman.
Traveldoc (another such database) says:
Transit passengers are required to hold a machine readable travel document and remain in the international transit area.
Unless passengers are eligible to enter Oman, the connecting flights for transit passengers must be booked on the same ticket.
Visa is not required for passengers who are travelling to Oman for tourism purposes provided holding a confirmed hotel reservation, health insurance and a return ticket. Maximum stay of 14 days.
Passengers holding a valid employment visa who have stayed outside of Oman for 180 days or more must obtain clearance from their sponsor and from the Royal Oman Police - Department of Immigration and Residence before travel.
Which, in your case, says the same thing.