A:Answer You can't connect the iPhone directly. HOWEVER, you can use your old computer as the bridge to the external hard drive... meaning, you can go from the phone to the external drive and never "store" the images on your old computer. These days, it seems that Apple wants you to run things through iTunes. Hope this helps!
BTW - Before doing anything else, you'll need to format the external hard drive to HFS+ using the Western Digital software. It's super quick and easy to do, just follow the steps.