When you open ES File Explorer (with your USB device connected), can you see any entries below the Download link? On my X7, I have sdcard and USB2010 . If I click on the USB2010, I'm taken straight to my hard drive. If there is nothing there, please click the / Device link, then the mnt directory. Can you check the last few entries in there? In mine I have usb_storage and then USB_DISK0 . If I click through those, I have my drive listed (with the partition's name as the "folder" label). If I click that, I can see the contents.
If your Android apps have not been updated by Google's Play Store, you may find a slightly different interface is presented. Open up the Play Store app, sign in if you haven't before, and open the list of installed apps. If you click on one, you should see an Allow Auto Updates or similar box to tick. Tick it. Wait as long as it takes for all apps to update. Reboot. Open the Play Store app again, once more bring up the list of installed apps. If any want to update, wait until they finish. Then return to ES File Explorer.
btw, is your external drive formatted with a FAT/FAT32 or NTFS partition?