I'm assuming that your cats are indoor only, have not had contact with other cats or animals in the past 2 weeks and that you have not had contact with sick cats. If these assumptions are true, an infectious cause for sneezing is unlikely.
Possible causes of ongoing runny nose and sneezing in cats are irritation, allergy, foreign bodies, infected teeth, nasopharyngeal polyps, and tumors in the nasal passages. Viral, bacterial and fungal infections (cryptococcosis, histoplasmosis) are additional causes that can occur without contact with other cats.
Irritants include cigarette smoke, dust, plants, carpet cleaner, new carpets or other furnishing that off puts vapors (formaldehyde, etc.), carpet cleaner, cleaning sprays, laundry detergent, cooking fumes, insect sprays, etc. Irritants can originate from outdoors through ventilation systems also. Most allergies are really irritation rather than true allergies. Sneezing due to allergies can be caused by pollens and are generally seasonal. Treatment is getting rid of the irritant or allergen if possible. Antihistamines and steroidal antiinflammatory drugs are generally effective at controlling the signs. Steroid eyedrops obtained from the veterinarian can be used as nose drops or systemic drugs can be used.
Foreign bodies are not common in cats because of the small nasal passages. Sometimes small parts of plants, feathers from toys, insects or other debris can be inhaled and become stuck. Sneezing is usually intense with the cat rubbing its nose on the ground or with a paw. A purulent ( smelly, cloudy, white, yellow) discharge can develops if the material is not sneezed out.
Infected teeth are not a common cause of sneezing. The upper teeth are rooted near the floor of the nasal cavity. Infections can cause inflammation of the nasal passages. Abscesses of the roots of teeth can drain into the nasal cavity and be sneezed out the nose. The discharge is likely to be purulent and sometimes bloody.Treatment is removal of infected teeth and antibiotics.
The cause of polyps is not well understood. The arise from the middle ear, Eustachian tube or back of the nasal cavity. As they develop, signs such as coughing, trouble eating and loud breathing develop in addition to nasal discharge and sneezing. Treatment is surgical.
Nasal and sinus tumors are not very common, but possible causes of sneezing in cats.
Early signs include sneezing and runny nose. Other signs develop with time. Treatment depends on the tumor.
The infectious respiratory disease agents can be present in cats and cause respiratory disease in times of stress. Herpes virus is the cause of rhinotracheitis in cats. Cats can harbor the virus for years.Bordetella bronchiseptica causes kennel cough in dogs and can cause respiratory disease in cats. Treatment depends on the specific cause.
Because of the large numbers of causes of sneezing and runny nose, a veterinary visit is indicated in cases that do not resolve on their own within a week or so.
Let me know if you have follow up questions.
Nasal or ophthalmic saline rinses are useful in flushing out irritants, allergens and other small particles. Cats are not fond of having this done and the fight can be counterproductive.
An alternative that may help is putting the cat in the bathroom with a hot shower running. This works best for congestion, but adds enough moisture to the air that it should help dilute irritants and sooth nasal membranes.
Antihistamines can help with sneezing, but I'd be concerned about them covering up signs of more serious problems. If you opt to use them do so for for no more than a few days.
Diphenhydramine (Benadryl), Chlorpheniramine (Chlor-Trimethon) and hydroxyzine (Atarax) are the antihistamines most commonly used in cats.
The dosage for chlorpheniramine in cats is 1-2 mg up to twice a day. This dose is taken from the Pill Book Guide to Medications for your Dog and Cat ( I am a coauthor) and cross checked from various online sites. The syrup preparation is preferred to get the small dose needed for cats. Sedation, vomiting, diarrhea and lack of appetite are the most common side effects. Stop the medication if sedation is excessive or any of the other side effects occur.