property Grid.OLEDropMode as exOLEDropModeEnum
Returns or sets how a target component handles drop operations

exOLEDropModeEnum An exOLEDropModeEnum expression that indicates the OLE Drag and Drop mode. 0 means no drag and drop support, 1 means manual support.
In the /NET Assembly, you have to use the AllowDrop property as explained here:

By default, the OLEDropMode property is exOLEDropNone. Curently, the control supports only manual OLE Drag and Drop operation. Use the SelectByDrag property to disable selecting multiple items by dragging. The SingleSel property controls the number of items that the user may select. For instance, if the SingleSel property is True, the user can't select multiple items, and so a single item may be selected at the time. If the SingleSel property is False, the user can select multiple items using the mouse, keyboard or both. 

The control provides the following options to define the visual effect when drag and drop items:

See the OLEStartDrag and OLEDragDrop events for more details about implementing drag and drop operations into the ExGrid control.