To my knowledge, there was little or no significant damage to any oil industry infrastructure, although oil exports from Oman were temporarily halted.
Oman, and Iran were hit hard by Gonu, as well as the cities of Fujairah and Kalba on the UAE coast on the Gulf of Oman. Immediately after the storm there were shortages of water and food, and no electricity. The death toll is 70, with a number of people still missing, including 10 sailors from a boat sunk in the cyclone.
The bathymetry of the two coasts of the Gulf of Oman affected by the cyclone is very different -- the water depth drops off quickly on the extreme southeastern Oman coastline facing the gulf, which resulted in more damage from waves and wave runup, rather than surge. Offshore of Iran, the water is shallow for quite a distance, resulting in surge such as that experienced along the northern Gulf of Mexico, rather than high waves.
Wave heights from Gonu were astounding, and even the day after the cyclone, were still causing new flooding in the UAE. Waves on the order of 10 meters high, or higher, were modeled to have affected the extreme southeastern Omani coastline, and wave 6 meters high were documented in Fajairah, UAE.
In Iran, surge from Gonu inundated somewhere between 300 and 1000 coastal villages, according to various news sources.
Even more damaging for Oman's coastline was the flash flooding. The narrow coastline is backed by a 3000-meter-high mountain range, and communities are built right over the many wadis, or dry riverbeds. Rain against the mountains caused tremendous flash flooding, which knocked out bridges and removed pavement from sections of coastal roads linking the communities. The flooding also knocked out the machinery that pumped the water supply to the capital, Muscat, leaving the city with a critical water shortage for several days after the storm. The flooding was so extensive that the city was described as a "lake" by one public official.
http://www.wunderground.com/blog/MargieKieper/comment.html?entrynum=166&tstamp=200706