The first and most important thing to consider is "what does the beer taste like?" The judge doesn't see the recipe.
Just because the beer touches wood does not necessarily make "wood aged" the best fit category for that particular beer. In any of the speciality category the special ingredient / feature needs to be front and center.
That said, based on the recipe I'd agree with the earlier poster. Old Ale might make sense. It is a category with a fairly broad range of possible interpretation, and a hint of oak would not be out of place.
Consider this - enter it in two categories.
Steve in St Cloud, MN
Cream of Three Crops Cream Ale
Jolly Pumpkin Bam Biere clone - sort of
Tap 1 - Tripel
Tap 2 - American Wheat
Tap 3 - Munich Helles
Tap 4 - Black IPA - from Lucid Brewery wort
Bottles - Long Winters Nap Barley Wine - 2012 & 2013, & some odds and ends
In the bullpen:
Long Winters Nap Barley Wine - 2014, Six Jolly Fellows Porter, Helles (rebrew)