The first thing to do is to get the bounding box of the Brep using ON_Brep::BoundingBox() and test to see if the point falls inside of it or not using ON_BoundingBox::IsPointIn(). This way you can quickly eliminate some points.
You can use ON_Brep::IsPointIn() to see if a point falls inside of a closed Brep. See opennurbs_brep.h for details.
You can use RhinoBrepClosestPoint() to see if the point is on an edge, or a face. See rhinoSdkUtilities.h for details.
To see if a line is completely inside of a closed Brep, create an ON_LineCurve from the points and then use RhinoCurveBrepIntersect() to see if they intersect or not. See rhinoSdkUtilities.h for details.