As the external enclosure's circuitry is most fried by the surge, it's worth dismantling it to see what state the hard disk inside is in. Check the chips below the hard disk to make sure there is no visible scorching. If the hard disk itself appears fine, then it's worth getting a USB to SATA connector (or enclosure) to see if you can access the hard disk this way.
If the enclosure has two hard disks inside (e.g. 2 x 1TB), these are most likely set up in RAID 0 and you'll probably need a PC with RAID support (or recovery software supporting RAID) to access the content, assuming the hard disks are intact.
Unfortunately, if the hard disk's own controller is fried, you will most likely need to resort to a data recovery lab to recover the content, which is usually not worth it apart from critical business data where the cost of losing the data is more than what the lab recovery cost would be.