The delete button is there, iirc, but it's grayed out. Deleting Unit Designs is a planned but NYI (not-yet-implemented) feature.
Edit: if you really want to get rid of some of them, you should be able to delete the corresponding files in the "C:\(UserName)\Documents\My Games\Elemental\Units\" folder (on Vista, if that stuff is on your c drive). I'd advise not having Ele running while you delete those files.