Copy these commands into TextEdit, replace the bracketed part with your username w/o the brackets and the quoted parts with the ext HD's name, retaining the quotes.
sudo chflags 0 /Volumes/"name of ext HD"
sudo chmod a+rx /Volumes/"name of ext HD"
sudo chown -R <your username>:admin /Volumes/"name of ext HD"
Launch the Terminal app in /Applications/Utilities/, copy and paste the first one into the window that pops up, and hit the return key. When the Password: prompt pops up, carefully type in your admin password, since nothing shows on the screen, and hit the return key. Copy & paste the other two, one at a time, following each with hitting the return key. You won't get the password prompt, since the initial one's good for five minutes.
Quit the Terminal app and you should be able to read and write to the ext HD. This assumes there's no OS or Time Machine backup on the HD. If there is, don't run the third command.