Oman Air offers flights to Salalah and a few other cities. Taxi service is also available in most towns. These are not valid for exit via land borders. Road passes are necessary if you are driving. Passports are not kept by the sponsor.
Oman also issues tourist visas for two weeks.
These are easily available to anyone working in another AGCC state, but not impossible to get elsewhere. They're interested in tourists, but they want rich ones. Backpackers are not exactly welcomed. We have nonstop service to London, Bangkok, Manila, Cairo, Johannesburg, Durban, Nairobi, Colombo, plus seven or eight destinations in India. Most of these companies do not have daily service, however, and most flights to Europe will stop elsewhere in the Gulf before continuing on.