As I understand you have currently one shared folder which is called "Server". If you now copy the data from the old drive in this folder, you will still have only one shared folder. But you can create additions shared folders in the GUI of OMV and point them to existing sub-folders in "Server".
In the picture you can see, how to select an existing folder when creating a new shared folder.

Thanks for your response! Let me try to be a little more clear. I will be moving the entire folder structure into this one shared folder. Will doing make all of the subfolders (which have been moved from the USB drive into this shared folder) inherit the "Server" folder permissions?
In other words, I have one folder on OMV: "Server"
Into "Server," I am moving the contents of /dev/sdx, which has a structure of, e.g., "/data/myname/subfolder/subfolder/subfolder" and "/Music/Artist[1]-[n]/Album[1]-[n]." I assume that all of the moved folders will also be shared? Is there any reason I should be a little more granular and create "data," "music," "movies," and "TV" folders before moving those individual folders over?