According to the Romania Ministry of Foreign Affairs, Turkish passport holders do need a visa, issued in advance, not on arrival. Without it, you wouldn't be allowed to board a flight to the country, either from UAE or Oman. However, you should be able to apply online, using the eVisa tool. As there is not an embassy or consulate in Oman, you are also able to apply from a nearby country.
Romania Embassy in Abu Dhabi
2nd Str., Nr.9, W(14/1) plot No.13 at Al Rodha Area
PO Box 70416
United Arab Emirates
Romania Embassy in Riyadh
Riyadh, King Fahad Quarter, Amin Al Rehany Street, Villa no.8
PO Box: 94319