I think that your birds could have a respiratory infection. I would personally isolate the sick birds. It could be a disease like Chronic Respiratory Disease, or Coryza. It is hard to tell the exact respiratory disease, however (and that's assuming that it is one- it could be caused by dust getting in the eye, or could be an eye infection).
If it's an eye infection or a respiratory infection, it would be a good idea to start antibiotics. Tylan50 is a good antibiotic for respiratory disease. Terramycin eye ointment could help if it is an eye infection. Even Penicillin could help an eye infection.
If it's a respiratory disease, keep in mind that your birds will likely always carry it, and could show signs again in times of stress. An eye infection should eventually clear up.
Most feed stores and TSC will carry Tylan 50 injectable, which can be given either as an injection into the breast muscle or by mouth, and oxytetracycline for the water. It looks like you may be dealing with MG or coryza. Is there a really bad smell near their heads? Clean the eyes and apply either Neosporin, Triple antibiotic, or similar ointment, plain with no pain killer as a tiny dot into each eye. You will need 5 syringes (3 cc) and 5 needles (22gauge) for Tylan, even if you give it orally to get it out of the vial. Here is a link you should read about the 2 diseases above: http://edis.ifas.ufl.edu/ps044