This just happened to one of my Pekin ducks last week (actually second time now) She's always been weaker than my others and has a tendency to walk slower and rest more often. Anyhow, she literally could not pick her head up, walking around like she was drunk like you said. Everything I read pointed to what is called Limberneck, or Wry neck, basically botulism. The good news is,she has recovered both times with a little TLC. Keep him separated,in a quiet non stressful place. You need to dilute his system with lots of clean water. Add a little apple cider vinegar to the water and if you have any vitamins with Niacin and Electrolytes that helps a lot. I use Rooster Booster. But any Feed supply store should carry poultry vitamins. I literally had to take her head and put her beak in the water and sometimes she would drink on her own and I would tilt her head up so she could swollow. Other times I would use a syringe and slowly feed her the water. I was vigilant and made sure she was drinking at least every half hour. Try not to stress him out too much though, because rest is also important. I kept her separate from the other ducks a day or two. And within 48 hrs she was good as new.
Good luck, hopefully he pulls through! Keep us updated.
