Slow and steady, Nat. Starting by doing what others here have advised; leaving it on him for short periods, rewarding with praise, treats - whatever he responds to - when he drags it around. Slowly increase the time it's left on him. Once he's used to it and moving freely, pick up the end and follow him around - let him take you anywhere with it. No tension, no pulling, no guiding, no coaxing - he has complete control.
Once this is under the belt (so to speak) start encouraging him to follow your lead when his leash is on by enticing him forward while you're holding it with treats, praise - again, whatever he responds to once you work it out. After that, baby steps with him walking beside you.
Remember, always praise, always treat, always encourage, always gentle. Let him go at his own pace, take it easy and make it rewarding. It will take a bit of time - but I guess you've got that with this baby. He's not going to be ready to go anywhere for a long time.
What happened to him makes me burn. No Jack Russell terrier would ever be that timid and frightened - they're so spunky normally. Poor little guy, I'm glad he's in your hands. Are his former owners going to be prosecuted?