Add different classes to the images that where uploaded with multi-upload
Go to admin/structure/file-types/manage/image/fields. Add a text field for the class. 

Now the difficult part is how you are going to get the class as an attribute into the img tag, or into a wrapper div. 

If you are using Views you can easily 'rewrite the output of this field' and do it in there.

If you want to render by view mode you can use Display Suite and a custom field template, or you can just forego Display Suite and implement your own custom template file for the file display : Displaying Media

And perhaps rethink your methodology. You can let your client use CKEditor and set the classes to the images right there where he has a proper preview of how it is going to display. You can add your own custom predefined styles that is selectable from a select list. It is also possible to right click on an image and set the classes on.