Vinegar is recommended for food poisoning. He might do fine with a bit of dill pickle or sauerkraut. Or some vinegar with honey in a glass of water.
Vomiting is the body's way to get rid of toxins.
Do not give your son milk products or dairy foods until his is much better and recovered.
Do give him juice and jello if he does not feel like eating. This will help him not to get dehydrated. If he feels like eating something, give him a plain biscuit like arrowroot biscuit or a plain piece of toast to see how he gets on.
The green coloured vomit is bile. It may be a good thing to give him a piece of toast only a little bites to see how he gets on.
Do make sure that he drinks his juices and water and no milk products.
Mayo should always be refrigerated. Sounds like he has food poisoning, it usually takes a few days for it to get out of the body.