Dragging the figure is trivial by clicking with the mouse to the title bar and dragging it. But this does not concern the contents of the figure, so I do not see how this could affect the lines.
You can simply use the ButtonDownFcn of the lines. I assume moveobj can be applied directly, but I'm not sure about this.
Looking in the FileExchange is always a good idea. Searching for "drag line" you find e.g.
- http://www.mathworks.com/matlabcentral/fileexchange/42284-drag-line-in-gui
- http://www.mathworks.com/matlabcentral/fileexchange/4179-draggable
- http://www.mathworks.com/matlabcentral/fileexchange/35438-drag-a-line-with-the-mouse
- http://www.mathworks.com/matlabcentral/fileexchange/33041-drag-and-dropline-objects
