What a sad life for that poor pup. It's wonderful that you're trying to make it better.
The easiest way to prevent a dog from eating socks is to keep the socks somewhere the dog can't get them. It might be inconvenient (can't just toss your dirty clothes randomly on the floor), it's by far simpler than trying to train the dog. At some point, if the dog is never permitted to take anything not hers and has her toys as the only play options, she may give up sock eating. Still, even that isn't guaranteed.
The easiest way to prevent a dog from eating socks is to keep the socks somewhere the dog can't get them. It might be inconvenient (can't just toss your dirty clothes randomly on the floor), it's by far simpler than trying to train the dog. At some point, if the dog is never permitted to take anything not hers and has her toys as the only play options, she may give up sock eating. Still, even that isn't guaranteed.