Here is one approach that should work:
- Create your new catalog.
- Import your files from each of your source discs to the new catalog. If you have duplicate files, this process should eliminate them since in theory Elements does not allow duplicate files in a single catalog. If this is the case, you may receive warning messages that certain files were not imported because they already exist in the catalog.
- Once all of the files have been imported, create a full backup copy of the catalog. This will backup both the catalog database files and all of your media files.
- Restore the catalog to your new external drive. (If you have a large external drive, you can create the backup and restoration on the same drive, but it would probably be faster to use separate drives.)
- During the Restore process you will be given several choices for the new location of the files. I suggest that you use the New Location option. You can then select (and/or create) a new main folder such as My Pictures and all of the existing folders from your various drives will be flattened and placed under the main folder. So you will be left with a main folder and a single level of sub-folders under it. If you need to maintain your folder structure, then you should use the New Location with Restore Original Structure option.
For more details on the Backup - Restore process, see this article.
Elements 14 can handle all of this.