I seriously doubt he's actually eating wood, though it may appear he is. Some parrots like to chew wood (especially the soft stuff they use for toys) into absolute splinters before they spit it out. Their beaks are amazingly dextrous, and they have a kind of control with them we simply do not with our mouths when it comes to chewing. Kiwi does this from time to time and it looks like he's eating it, but he's really not. Since wood isn't digestible, you would be able to see splinters in his poo if he were actually eating it.
Excessive chewing is actually a very common hormonal behavior, and actually isn't a bad thing (there are far worse ways they can express they are hormonal). I would suggest giving him more chewing things (more wood toys, newspaper, toilet paper rolls ect...) to keep him distracted from his hormonal urges in a positive way before he decides to start chewing fingers instead.