I don't ever consider a "dirt-bike" to be street legal. What you are looking for is a dual-sport or adventure bike.
Unless you are an advanced rider I wouldn't consider riding any dual sport bike in sand dunes. The additional weight and probably 50/50 tyres are going to make it very difficult.
The 650 BMW or Kawasaki is going to take you anywhere you want to go. Apart from the sand dunes, most of Oman is reachable via rough gravelly or rocky trails, and either of those bikes will eat that up without a problem. The rest of the country is covered with very well maintained highway.
I rode 570 KM last monday, with occasional short runs off-road and my KLR was perfect (Except for the damn saddle
). As you go along the highways, you see many many signs for small villages. They seem to be served by groomed dirt roads and any of them could lead to somewhere interesting.
Of course there are the most popular tourist spots like the wadis and sink holes, but they tend to get swamped by Omanis and their 4x4's. I prefer to keep away from all that.
Adventure riding is a very small part of the community here. There are many Harleys, Dirt Bikes and Sports bikes. Most of them don't go exploring.
Anyway, if you want to see it all, get a 400 to 650cc bike with 50/50 tires and you'll have no problem.
Bring any gear you think you'll need with you. There is almost no mc gear available here, and if it is, it's low quality stuff.
Good offroad or ADV boots
A helmet (law)
Good vented gloves
Mesh armored gear
A camelbak or at least a day pack to carry water.
Bandannas for covering your neck and wiping sweat.
Sunglasses that fit in your helmet.
It's cooling down now that winter is coming, but it was still 41c here last week with 80%+ humidity. Not sure when you're coming, but it never gets much below 25c.
It's still the middle east, so the drivers can be, shall we say, a little thoughtless at times. You really have to keep your wits about you. Armoured clothing is just an extra bit of insurance.
I'm pretty new here myself, but I'll help you all I can.