I've done a bit of traveling myself and can definitely help with this. Yes, you can apply for an Oman visa online from the U.S., including from Alaska. The Sultanate of Oman has streamlined this process through their official eVisa platform. You'd need to fill out an application, submit a scan of your passport (ensure it’s valid for at least six months from your planned entry date), and provide a passport-sized photo.
One piece of advice: double-check the type of visa you need based on your travel purpose—tourist, business, etc. Also, keep in mind that processing times can vary, so it's wise to apply a few weeks in advance of your trip.
I found consulting the official Omani government site or reliable travel websites useful to verify any changes in visa regulations due to international circumstances. If you have more specific questions about the application or travel in Oman, feel free to ask. I'm here to help!