This really sounds like pica to me; please read the ASPCA's article on pica here. However, I'll talk about some other things we can do to help the problem, and then we'll get back to pica at the end.

First things first. You must begin picking up ALL clothes, socks, towels -- anything the dog eats. In a few other comments, you said things like "We try, but it's hard" and "There are kids, so it's hard." I can imagine how difficult this must be, but as other posters have said, it HAS to be done. If there are socks out, he will eat them. We're going to prevent the dog from practicing this behavior by changing something in the environment.

Now that that's done -- has the veterinarian done blood work on the dog as part of his surgeries? Was there anything strange on the blood work? Sometimes a hormonal imbalance can cause very strange behavior. I think you've probably had blood work done, but if not, I would really recommend doing this to look for any abnormal values.

Next -- how's the dog's exercise? Dobermans are very active dogs, so if he's not getting adequate exercise, I'd recommend upping the exercise. This doesn't directly address the problem you're seeing. However, it's in the category of "Can't hurt, might help." IF the sock eating is related to an excess of energy or anxiety (I really can't say if this is the case, but I'd like to consider all possible explanations for this bizarre behavior) then exercising him more COULD help.

Fourth -- Let's audition lots of safe chew objects for the dog to chew on and find the ones he likes best. Watch your dog playing with the toy to ensure he does not eat it. Chewing is normal dog behavior. You'll want indestructible plastic toys (think Kong-type toys) and toys that are large enough that they cannot be swallowed. Avoid very hard toys (such as antlers) as these can chip the dog's teeth. Petexpertise has a great chart comparing different toys.

Bonus points if you stuff his meals into the toy, so that he must spend time extracting the kibble. The goal is to give your dog many safe things to chew on. This will allow him to exercise his natural urge to chew. It should keep both his mouth, and his mind, busy.

Now, onto the training. As others have suggested, you need to train a very strong "don't touch!" or "leave it!" command. Watch Kikopup's "Leave It" video here.

I want to stress that training a "don't touch!" command will only work as long as you are present. If you are absent, the dog will still gobble up the sock. This command will not teach him that socks are universally forbidden.

You should also teach a strong "come!" and a solid "drop it!" or "give!" command.

If all else fails --and this is a life-or-death issue-- there's always the option of using punishment training, but this is an area that I am not personally familiar with. Basically, you would want to use an aversive (such as a citronella collar) when the dog goes near the toy. However: if your dog is sensitive, this will really scare him, and we don't want dogs to feel scared when they are learning. Punishment also does not teach the dog what he should do instead of sock-eating. Ideally, we want him to learn that it's better to ignore socks, because they're stupid and boring when you have lots of other fun toys to play with.

I do, however, agree with the other commenter that this is most likely a manifestation of pica, in which case, it's a compulsive disorder, and you'll be limited in what you can accomplish with training; basically, you'll never be able to 100% trust the dog when he's left alone in a room full of socks. Most commonly, I've heard of dogs with pica eating rocks, in which case the dog must always wear a basket muzzle when he goes outside.

I also want to call attention to this excerpt from the ASPCA article:

Train your dog to perform a specific behavior, such as sit or bark on command, whenever she discovers anything similar to the nonfood items she usually tries to eat. Teaching a new skill will enable you to prevent your dog from eating dangerous inedible objects and reward her for some other behavior you like better. Your dog can’t bark at an object and eat it at the same time!

Basically, we are teaching a replacement behavior for sock eating; we're saying to the dog, "instead of eating this sock, you should bark at it, and earn a tasty treat!" I like the idea of teaching the dog to bark at socks because then you would immediately know when he's found one in the house.

Do not be afraid to use the most fabulous, amazing, incredible treats (parmesan cubes, anchovies, cheetos -- seriously, anything your dog LOVES.) Currently, in his mind, socks are VERY VALUABLE items. We need to use food that he likes even BETTER than socks in order to make the training more potent.