What are these green balls hanging on my tree?

Question

they're light green come once a year deer eat them and if they get stepped on theres this gross brown gunk comming out of it

Answer 1

What kind of tree is it?  Could it be a bloom or fruit that is specific to that tree?  If you know it isn't natural to that tree or if the green balls are on several different trees then take a sample to the nearest library.  Perhaps you can contact the agiculture dept. of a local college or university?  

Look up hedge apples and monkey balls online and see if they are the same fruit.

Answer 2

probably fruit

Answer 3

Softball-sized and very wrinkled? That would be osage orange.