Finding work in Oman will take some doing, but it can be done. However, be warned that gaining employment as you pass through the country is not going to be possible. Jobs for Europeans are generally limited to upper management or highly skilled professions. Unless you are willing to work for very little, best to arrange for these jobs before landing in the country. The majority of the lower level jobs are occupied by expatriate form the sub-continent.
To be able to work in Oman foreigners will need to get a residence permit first. While it not uncommon for people to land in Omen on a tourist visa and then seek employment, employers caught employing such illegal workers face substantial penalties. So, not many employers are willing to risk it.
The one occupation that Oman has a strong demand for is qualified English language teachers. They are needed at the numerous English language centres and government universities. There are also an increasing number of international schools as well as private schools which require qualified people to teach at all levels. Due to the stringent visa process and teacher hiring cycles, it is best if a contract is acquired before landing in Oman. Teaching salaries in Oman are competitive with those in the region, while the cost of living low, especially if the location is outside of Muscat.
Other jobs for expatriates in Oman can be found in the oil, gas, petroleum, medical, and construction sectors. Engineers, specialists in the field of IT, and project managers are especially in demand.