You might be surprised to know these growths on oaks are galls caused by different species of gall wasps. Gall wasps are insects which are quite small, and unlike the larger wasp species you may be familiar with, they do not sting people.
Do gall wasps sting humans?
Gall wasps won't sting persons or animals. Their sting isn't designed for attack, it's actually simply a tube that lays eggs. It can pierce through woody tissue but the wasp won't use it to defend itself.
Are gall wasps harmful?
“Oak apple galls” are leaves that have developed into a thin sphere because wasps have laid eggs inside of the leaf. Inside the gall is a tiny wasp larva. Most galls, especially on leaves, do not hurt the oak tree, and the wasps aren't harmful to people either.