Try restarting in Safe Mode per the directions in Safe Mode. Do this restart with all external HD's physically disconnected. If you have a wireless keyboard, it's wise to plug in the USB connection (charging cable) it came with and do the restart with that cable attached. After you have restarted in Safe Mode please re-start normally. Introduce 1 External Hard Disk and see if Finder and Disk Utility finds it. If it does, rinse and repeat with the remainder of the EHD's.
If no connection is made please answer the following:
Do you have any of the following third party apps installed on your Mac?
• Antivirus Apps
• Cleaning Apps
• Security Apps
• VPN Apps
• Maintenance Apps