I thought that part when Fern was there when the animals were singing and could understand them was strange, then the other times she was with Wilbur he didn't talk to her after that, just grunting and oinking like a normal pig.
shareIn the book, Fern's mother is concerned about this and takes her to the doctor. The doctor comments that perhaps children like Fern are simply more attuned to the animals than the adults are.
My take is that Wilbur didn't talk to her directly - just to the other animals, and when they weren't around, there was no need for him to say anything.