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
Primary - Helles
Conditioning - Orange Blossom Mead, Long Winter's Nap English Barley Wine
Tap 1 - British Golden Ale
Tap 2 - Wiessbier
Tap 3 - American Pale Ale
Tap 4 - 6 Jolly Fellows Porter
Tap 5 -
Tap 6 - Yorkshire Strong Ale
Bottles - Jolly Pumpkin Bam Biere clone, Long Winters Nap Barley Wine - 2012, 2013 & 2014, Flanders Red,