The easiest way, I think, is to use a TListView rather than a TStringGrid/TDrawGrid because it has built-in image support. Just add the images to an ImageList, and when you add the data as TListItem you specify the image index. In the OnMouseDown or OnClick event you can determine whether a click occured on the image and switch to the next image (or whatever index you want).
If you insist on TStringGrid/TDrawGrid you must owner-draw the cells.