Mouse drag with specific angle

It would be easiest if you defined this problem as confinging an object to an arbitrary line rather than a specific angle. From your drawing, the easiest way to get the line would be to add an empty game object to your wall at a point other than the pivot point and at the same distance from the camera. Then you can define the line by a point and a direction. For dragging, you can find the closest point on the line to the mouse cursor, and position your block at that position. The closest position on the line can be done using Using the ProjectPointOnLine() method in the Math3d class in the Unity Wiki. So given 'scanPos' is the position of your wall, and that 'secondPos' is the Transform of an empty game object on the wall that defines the line, here is a bit of untested changes to your code:

 function OnMouseDown()
 {
     screenPoint =Camera.main.WorldToScreenPoint(scanPos);
     offset = scanPos -Camera.main.ScreenToWorldPoint(Vector3(Input.mousePosition.x,Input.mousePosition.y,screenPoint.z));
 }
 function OnMouseDrag()
 {
     curScreenPoint =newVector3(Input.mousePosition.x,Input.mousePosition.y, screenPoint.z);
     curPosition =Camera.main.ScreenToWorldPoint(curScreenPoint) + offset;
     var = dir = secondPos.position - scanPos;
     transform.position = Math3d.ProjectPointOnLine(scanPos, dir, curPosition);
 }