You are correct that WOL is Owl. The joke here is that Owl is supposedly wise and well-educated, especially compared with the other, illiterate occupants of the hundred-acre wood. But in fact, although he puts on airs and graces, he's not very clever at all and can't even spell his own name, nor differentiate between capitals and lower-case letters.
The reason Owl writes letters to himself is because none of the others can read at all, so he has no one else to write to. Writing letters to himself also fuels his own sense of self-importance: it's not hard to imagine him boasting to his friends about all the letters he receives. Of course, he's cheating by writing them himself but Owl, like most of the other characters in the book, is very immature.
This leads to the other joke here which is that letters written to yourself would not really be "unexpected". But Owl would claim they were, to keep up the pretence that he can feel important by receiving letters.
The immaturity and relative ignorance of Owl and the other characters is a key part of the appeal of these books. Originally written for children, although still very enjoyable for adults (including me), they allow the child enjoying the story to feel a sense of superiority to the characters. They require a level of literacy beyond that of the very young so most children who enjoy the stories would, presumably, know how to correctly spell "owl", thus getting the joke and a satisfying sense that they know more than the supposedly wise Owl.