Firstly, that is one of the nastiest menus that I have ever seen. I know it's not your work, but this is a fantastic example of what happens when UX is not considered.
That said, I can think of no interface that will make a menu with those options usable. You have to deal with the underlying issue, that the category groupings need to change to be able to handle this well.
Many items that would logically fall under many of the categories there, which is the problem. Category groupings should be orthogonal. Which is a technical way of saying that the category groupings should be chosen so that all items clearly fall into one category.
For example, if the groupings were: Kitchen, Bedroom, Bathroom, and Office, you would have little confusion about what category to look in for a plate, or a pillow.
So from here, you need to take a step back and try to work out what items there are, and how to group them. From there, you should find that you will have fewer categories and that the menu problem has mostly been sorted out already.