The fact that he has pulled all his tail feathers out indicates there may very well be something very wrong with him. Possibly he is in some kind of pain.
You will have to take him into see an Avian Vet in your driving area to have him checked out for infections and/or parasites or something else physically causing this aberrent behavior.
Being wobbly may have something to do with the lack of tail feathers, and it may be a part of what else is going on with him.
PLEASE DO NOT TAKE HIM TO A REGULAR DOG AND CAT VET AS THEY ARE NOT LICENSED TO TREAT BIRDS AND CAN DO WAY MORE HARM THAN GOOD SINCE THEY ARE NOT FAMILIAR WITH A BIRD'S PHYSIOLOGY. Birds have hollow bones and no fat on their bodies, so any overdoses of meds can and does kill them. A dog and cat vet is used to treating animals who have fat reserves where overdoses of drugs can reside while they are being processed. In birds, there are no such reserves, and drugs go directly into the liver and kidneys to be processed sometimes causing failure of one or both organs.If not failure, then lives are shortened because of damage to one or both. Play it safe and take birds to bird vet and dogs and cats to dog and cat vets.
So, your bird needs to be seen by an Avian Vet, and you'll need to find one immediately. Tracie has a link on site to help,( Find an Avian Vet ) and there is always the internet and phone book to help with finding one. Anyone who has birds has to have at least one Avian Vet to take care of any sick or injured birds because we never know what could happen next. Though dog and cat vets are NOT licensed to treat birds, somtimes people take them there anyway, and if you lose your bird, you will have no legal recourse because you voluntarily turned bird over to someone not capable of treating it.
Thanks for writing and let us know what the Avian Vet has to say about your bird's problem.