In a senior dog there are a few possible things that could be causing the symptoms you have described.
Dental disease would be on the top of the list. When there is infection in the mouth this can cause not only a foul odor and thick saliva but it can also lead to problems with the nasal cavity and throat. Dental disease can also lead to gagging and dropping food.
Now this can also happen in the reverse order meaning if there is infection, polyps or even cancer in the sinus cavity,this can lead to smelly breath, nasal discharge and irritation of the throat.
When we see trouble with gagging especially when eating and eaith a change in barking or not barking at all in a large breed senior dog we also worry about Laryngeal Paralysis. The following link will cover this problem in more detail. LINK
I think this is really going to take a hands on exam to get a good look at the teeth and to check for signs of laryngeal paralysis. If there is infection in the mouth a good dental cleaning may be needed however if cleaning is not an option then antibiotics alone may help.
To help with his nose you can try using a saline nose drop. In our practice we recommend either lil noses or little remedies both of which are nose drops made for infants. 2-3 drops in each side of his nose twice daily. This can cause them to sneeze out a lot of discharge so you may want to do this outside.
This time of year allergies can also cause nasal discharge and oral Benadryl can help with this. This is dosed at 1 mg per pound of body weight every 12 hours.
I hope this helps give you some direction. Please reply back if you have additional questions and I will be happy to continue.
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