[How to] Change Order of Menu Items in Dropdown Menu
Dropdown Menu Widget is no longer maintained. Please use it at your own risk.
Dropdown menu widget automatically generates pages and categories menus. While generating page menu, it uses Page Order specified on Add New Page screen.
Unfortunately, for categories, this feature is not available. However you can still order your category items, using Menus under Appearance.
To achieve this, simply add a custom menu, and add all categories to your menu. Sort menu items as you like them to be.
Then while adding your dropdown menu widget, select your custom menu from menu selection box. If you are adding the menu using php template tag, you can use custom menu tag explained here.
I hope this helps you about creating your own menus.