Rhino's CageEdit command's closest equivalent in grasshopper is Spatial Deform. The combination of an already powerful command with grasshopper's interactive nature makes this a very complicated and memory intensive tool to figure out and use. Other than this Q&A and this demo, I really can't find a good example of using Spatial Deform, so here goes a basic introduction:
To use Spatial Deform, you'll need to attach the following:
'G' - the rhino geometry to deform
'S' - a series of points that will define the cage
'F' - the forces applied to each of the points in 'S'
'f' - a falloff equation
Now this script takes advantage of Kangaroo's removeDuplicatePts. If you don't already have it, get it at their website.

