From what I can tell is a compatibility issue between WordPress 2.5.1 or 2.5.2 and Divi.
Update your Divi theme to the latest version and all these should be solved.
Remember to backup before updating, and get ready to fix some css issues after update ( mainly forms, but the Divi update can also affect menus, blurbs and so on ).
Also, try contacting the guys from elegant themes – they can be pretty helpful in situations like these.
For a quick and messy fix: try disabling the sections you can’t delete ( Mouse 2 over the section->Disable ). This will not fix the issue, but it will make the unwanted sections “disappear”.