How do I give my 5 year old son who has cerebral palsy a nasal rinse? He has asthma but he is also allergic to eggs, wheat, nuts, corn.

Drops over rinse. If swallowing & gagging are issues with your son you should probably stay away from the large amounts of saline involved with rinses. In his case this may lead to aspiration pneumonia. Instead put a few drops or a few sprays of saline mist in his nose. You can try gently bulb suctioning out mucous after putting the saline in his nose.
Maybe not. One option is simply to try a nasal saline spray, instead of more aggressive rinse, although the rinse is very gentle. Consider the saline spray that contains xylitol, which has many benefits. These include preventing various bacteria from adhering to the nasal lining, as well as helping our bodies kill some bad bugs. Xylitol tastes sweet, so kids love the spray :)).
Mgt/workup. If your son has asthma and food allergies, he may also have nasal allergies to dust, pollen and other allergens. I would advise an allergy panel test called an immunocap test which can be ordered along with his other bloodwork. There are many types of applicators for nasal saline, and I would recommend using a gentle mist with gentle suction to remove the mucus.