Firstival, I would recommend to rid of inline event handlers (e.g: ondragstart="drag(event)
").
As I can see, you use html5 drag-and-drop API, which is good but will have issues with browser compatability (for instance, it won't work in IE < 10).
To have it work nice and well in most browsers I would recommend using such jquery-ui widgets as sortable and draggable with touch-punch which in most cases will do the work of handling touch events.
Should you need the example of code invoking draggable functionality, you can find it on jquery-ui website.