If the oak is subtle enter it as a Irish red ale.
If the oak is noticeable enter the beer into the oak category.
if your not sure you can always enter both categorys
Lookin good! How long have you had your kegerator? I have the same one and I've been having trouble with ice building up between the back plate and the copper tubing, and I even have a small dehumidifier in there. I'm wondering if a fan would help