Short version: How can I drag Link 1
into one of the dropdowns under Link 3
in this demo? http://jsfiddle.net/Gdadu/2/
Here is a fiddle that shows a few points that can help you with your implementation: http://jsfiddle.net/Gdadu/13/
It is far from perfect, and as pointed out in the comment, there is a few logical problems also with "sorting everything everywhere" :) Things not working here are sorting nested li's back to top level, sortables on nested ul's, ... but I think they are sketched out there. Distinguishing the sorting from the dragging might be one thing necessairy with jqueryui's current status. Also I shortcut your excellent css solution for the submenus and made them javascript based as to simplify things a bit.
But: You can drop link1 inside link3 or link3's nested ul ;)