You could enable the functionality by first configuring the corresponding RadListBox(es) to allow Reorder and/or Transfer and then setting the EnableDragAndDrop property to true.
In addition to all corresponding events that fire on Reorder/Transfer RadListBox supports a few solely drag-and-drop events.
At the client, these are:
OnClientDragStart - fires when the drag-and-drop operation starts. Can be canceled.
OnClientDragging - fires while an Item is being dragged. Can be canceled.
OnClientDropping - fires before the dragged Item is dropped. Can be canceled.
OnClientDropped - fires after the dragged Item is dropped.
After a successful drop the corresponding Reorder and Transfer client-side events fire.
At the server, the Reorder or Transfer events fire only if the AutoPostBackOnReorder or AutoPostBackOnTransfer properties are set to true.