If I find myself caught in a sand storm, what should I do? Should I sit it out, or try to keep moving somehow? Can this depend on the severity of the sand storm?
Sandstorms (or, here in the southwestern part of the US, dust storms) impair the ability to see and breath. The winds also carry heavier debris. Because the storms often occur when it is hot, the wind can contribute to dehydration. The reverse is also true--cold, winter dust storms occur in some places, and hypothermia can become an issue.
Fortunately, most of the time, there is advance warning. Even if you don't hear the alert, you can see the wall of sand or dust moving your way.
There are related conditions of which you'll want to be aware. These storms are often accompanied by lightening and rain. Particularly in desert regions, the rain can cause flash flooding.
You asked if the precautions can depend on the severity of the storm. Yes, the size and intensity of these storms vary greatly. When they are gathering steam, it's often not possible to distinguish the storm that has the potential to be more dangerous. Don't be misled, though--these storms are changeable and have the potential to become both fast moving and destructive.