Dr Mike, crikey, That's a question and a half!
As I understand it, the US has stepped back from the lead role in the Libya conflict, and it's the British who are putting boots (well, helicopters) on the ground. If there's an escalation of the operation I think it'll be British, French and other European troops involved (at least most visibly), so there'd be no extra reason to be worried about being American.
As it stands, Oman is not considered particularly dangerous for foreign travellers. The nation has strong ties to the west and although not as open as say Dubai. Check out a previous Answer about safety in Oman, I think it still applies.
Of course if there is an "invasion" that'll cause trouble and it will certainly be time to re-evaluate.
Phil about 8 years ago
Have lived here for a year considering this and also what would happen if war with Iran happens. Still have no clear answer. When things were heating up we noticed more war jets flying over in formation, attack helicopters flying low and many more British soldiers(and some American). But now things seem calm again.
Been trying to find out where Oman will stand with military action from the West but this is still not clear. Aside form possible protests Oman seems quite safe. Calm in the center of a storm. about 7 years ago