Can I take my disassembled desktop computer on a flight?

You should not have to pay duty, as personal effects are duty free, but you would note it on your declaration and anticipate questions, as all baggage, both carry on and checked, is x-rayed in Customs.

What to expect when I arrive - Muscat Airport

Oman has strict laws governing the import of items into the country. It is important that you are familiar with the restrictions before you travel.

After you have collected your baggage from the carousel follow the signs to the exit. You will pass through customs clearance. At this point all baggage, including hand baggage will be x-rayed and may be searched. If you have anything to declare, you must declare it when your baggage is x-rayed.

And, if you are relocating to Oman:

Used household goods and personal effects are duty-free provided goods have been owned and used by the customer for a minimum of 6 months....

As others have suggested, it's a good idea to take along a copy of the purchase invoice or receipt, just in case.