Do you know what the fluid is on the neck? Is it saliva?
What size needles and syringes do you have?
Well I am not sure what kind of places these would be in multiple different locations. Your needle will only drain fluids that are very thin. The best thing is to get your vet to show you how to drain this place, just because you don't want to hurt him or yourself. But to try it at home, have one person hold the dog, especially the head, probably even muzzle him so he can't bite anyone. Then scrub up the location with an antibacterial soap and water and then rinse. Then swab with some rubbing alcohol. Then if you are right handed, hold the swollen area with your left hand (index finger and thumb), this will stabilize it so you can find where you want to drain. Use your right hand and find the soft fluid pocket and insert the needle with syringe into the softest area. Pull back on the plunger and drain the fluid. You only have a 3cc syringes, so there may be more fluid than that. You can remove the syringe and leave the needle in the skin while you empty the syringe and reconnect it to draw off more fluid. Possible complications are: 1) you don't want to hit the jugular vein or carotid artery in the neck, you can get more bleeding than you anticipate 2)when you introduce a needle into this swollen area, you can introduce bacteria and get an infection 3) the dog can try to bite you or whoever is holding and then you have to go to the doctor.
So all I can say it is best to take him to the vet and your vet can describe better how it is best for you and your dog for you to do this at home.
Hope this helps,