My friend is a certified Dog Listener and is usually the one that they give these types of puppies to when they come into the shelter. She got a pack of puppies / adults a few years back that had been abandoned on a farm and had lived wild for about a year, with the puppies never having human contact (they were about 9 months old).
What you are describing is a combination of no socialization and fear submission. My first dog, Ellie Mae, had serious fear submission and would squat and pee when you tried to touch her. But what to do? I'll try to put on my "dog listener" hat for a bit here.
I think they need concentrated efforts to bring them around. All 3 are out of their "norm" and you need to give them confidence with their environment. You do this by bringing out their pack instinct in them, which means you must place yourself (and any human in your house) into a pack leader role. A pack leader does the following:
The alpha always eats first and controls what the others eat: When you feed them, be very obvious that you are preparing their food bowls, then when ready, stop and eat a nibble of food yourself in front of them. It can be a cracker or other little tidbit but you must eat something. Once done, put the food bowls down and walk away. Any food that they haven't eaten in about 15-20 minutes should be removed. Never, never, never free feed a dog, as it puts them in charge of their food, which is something only an alpha can do. It is remarkable how well this little trick works with them!!
An alpha leads the hunt: For a normal dog, you should never allow a dog out the door in front of you when you take them for walks. Stop them at the door, make them sit, then walk out in front of them. But your puppies have a problem with collars and leashes still. Dani would put the collars/leashes on them for a while and let them drag them around the house to break them of their fear of them (sounds like you are doing this). But as alpha, you lead the hunt, therefore it is your decision when they go for walks. Work on each individually and as hard as it might be on them, you must decide when they go for walks. If you allow them to choose, they win. Other trainers will suggest you tempt them with treats when they do something right. I'm not sure that this is true to form with dog listening, but could be a way to get them to follow.
An alpha makes the decision concerning flee / fight /fright. For the fear submissive puppies, don't cater to their fears, as you are telling them it is OK for them to make that choice. Be very calm and gentle with them and reward the heck out of them when they follow your lead. Calm them in a soothing voice then ignore them until they come around. They instinctively want to please you - that instinct might be deeply buried but it is in there. This technique works very well for those dogs that feel the need to bark at everyone that comes to your door or walks by your house. Thank them for warning you of the danger then ignore them. If they continue, you remove them to a place where they can't bark. I'm not exactly sure how to convert this to fear submission.
An alpha makes the decision on who and when to greet when they return from a hunt. When you enter the room with the puppies, do not immediately go up to them and greet them. This is what the lesser dogs do in a pack and by doing this, you place them over you. When you go into the room with them, don't make eye contact and ignore them for a while (up to 10 minutes). Go about your business and when they seem more relaxed, then reach out to touch them or talk to them.
When we found Ellie Mae 20 years ago (our fear submissive dog), we didn't know about dog listening but by instinct did a lot of these things with her. Our biggest mistake with her was giving into her fears by catering to them (oh, poor Ellie Mae is afraid of the thunder, lets cuddle with her). She didn't get over her fear of storms until we stopped catering to her fears many years later.
The bottom line with this advice: if the puppies feel that they are part of a "pack" and you are their leader, they will want to follow your lead. Their bad behaviors will disappear over time, but don't expect to see overnight success with them. Some things will get better immediately, but some of the more ingrained issues can take months to fix. It's all about building up their confidence and doing it through the language they understand. You might have a long road in front of you.
I have to recommend the book, "The Dog Listener" by Jan Fennell. I've just given you the condensed version of the Reader's Digest condensed version. She has a lot more specific examples of things to do in her book.