Air & Car
British Airways
www.britishairways.com
Flies from various UK destinations via Heathrow, London, UK - direct into Muscat. (There is a stop in Abu Dhabi - but no exiting plane).
KLM
www.klm.com
Flies from various destinations in the UK, via Schipol Airport in Amsterdam, Holland to Muscat. (This one has good rates if you book early and good times from Aberdeen).
Gulf Air
www.gulfairco.com
Flies from Gatwick, via Bahrain to Muscat
Emirates Airlines
www.emirates.com
Flies from worldwide destinations :

Australia - direct to Dubai, then onward to Muscat

Singapore - direct to Dubai, then onwards to Muscat

UK - from Glasgow, Birmingham, London (plus others) direct to Dubai, then onwards to Muscat

USA - Direct from Houston and New York into Dubai, then onwards to Muscat.

Plenty others as well!!!
Etihad Airlines
www.etihadairways.com
Flies worldwide into Abu Dhabi and onwards into Muscat - 

From Sydney direct

From London direct

Any many other options.
Oman Air
www.oman-air.com
Oman Air is a new route to Muscat (as the National Airline) and check with travel agents as to when routes open and rates.
Azerbaijan Airlines
www.azal.az
From Baku to Dubai, then connect in Dubai on Emirates / Oman Air etc onwards to Muscat.
Thai Airlines
www.thaiair.com
Thai Airlines have opened a new route from Bangkok to Muscat.  Bangkok is a good hub for flights from the Eastern Hemisphere. Please check the Travel Agents for details and costs.
Air Arabia
www.airarabia.com
Flies from various destinations in the Middle East.  Fares are cheap if booked early.  Limited flight times.
Jazeera
www.jazeeraairways.com
A Private Middle East Company Airline which operates cheap flights in the Middle East.  Not sure if times work for wedding.
Swiss Air
www.swiss.com
Flies into Muscat from European destinations. (Have very little info - sorry!)
Lufthansa
www.lufthansa.com
Flies from Europe via Doha, Qatar into Muscat.
Qatar Airways
www.qatarairways.com
Flies from Doha, Qatar into Muscat.
others
I am sure there are other airlines which fly via various routes into Muscat and other Middle East locations.  I hope this page is of help to you.  If you find any brilliant deals - can you let me know so I can tell others about them.
Car - Driving to Muscat
If you are driving to Muscat, you will most likely be coming from Dubai. 

Some guidance is as follows:

You will need to have car / vehicle insurance before crossing into Oman.

You will get an 'exit' stamp in your passport at the UAE border, and then have to park your car / vehicle at the Oman Border post (a large building). Inside the building you will receive your entry visa for Oman.  A rather simple process but can take 30 minutes if your lucky!!  Otherwise you can source your visa in Dubai before hand.

Keep an eye on your fuel - fill up when you see a petrol station!

Take plenty of water with you.

Drive safe!