I am currently training my 4th dog right now, so I sympathies with this situation! My puppy would chew EVERYTHING, and still does sometimes. I found that the only way to stop her was to give her a chew toy with a flavor, or something specifically for teething. I just got her a regular chew bone and she loves it.
The best thing to do, because you have other dogs, is allow her to chew on a bone in his own crate.
I know you said you cant crate train him, but it really is essential to letting him how his place in the house and pack with the other dogs. If he barks and cried, you ignore him. That's the only way, and the sooner you do it the better. Make sure the crate is a nice place for him, and praise him when he is in it, and this should help. If he has separation anxiety I suggest leaving him in his crate for short periods of time and ignoring him, then allow him out. Then gradually leave him for longer each day and he should get used to being alone without getting distressed.
Hope this helps. A really good person to look to/read about when it comes to dogs is Cesar Millan. I've trained all 4 of my dogs following his guidance and they are wonderfully well behaved!