|OK, the issue is pretty simple.|
In OE there is a setting to determine the location of the "store" files - i.e. the data files that hold your email. There is a different store file for each folder in OE.
The processes you are using are copying those store files to your external drive, (which is an acceptable backup).
However, when you try to "open" those files Windows has the extension for those files as belonging to OE, so Windows launches OE. However, the settings for the location of it's store files is unchanged. So, you will still see the "current" messages on your machine.
To see the messages in the backed up store files can be done, but will be problematic. You could either 1) change the settings in OE to point to the backed up files or copy the backed up files to your current store location (back up the originals if you don't want to lose them).
But, doing that may be more trouble than it's worth. If you were to receive any new email while connected to the backed up store files, those messages would be saved there rather than the current store files.
The full Outlook allows you to create archives and open those archives independantly of each other.
I don't have OE on the computer I am using at the moment, but you might want to check any export functions to see if there are any options to export messages in a format that you can read. At the very least you can "copy" messages out of OE into a folder. Then each message is a separate file that you can open and view.