Here is the quote from the BJCP Guidelines:
Comments: The base beer style should be apparent. The wood-based character should be evident, but not so dominant as to unbalance the beer. The intensity of the wood-based flavors is based on the contact time with the wood; the age, condition, and previous usage of the barrel; and the type of wood. Any additional alcoholic products previously stored in the wood should be evident (if declared as part of the entry), but should not be so dominant as to unbalance the beer. IF THIS BEER IS BASED ON A CLASSIC STYLE (E.G., ROBUST PORTER) THEN THE SPECIFIC STYLE MUST BE SPECIFIED. CLASSIC STYLES DO NOT HAVE TO BE CITED (E.G., “PORTER” OR “BROWN ALE” IS ACCEPTABLE). THE TYPE OF WOOD MUST BE SPECIFIED IF A “VARIETAL” CHARACTER IS NOTICEABLE. (e.g., English IPA with Oak Chips, Bourbon Barrel-aged Imperial Stout, American Barleywine in an Oak Whiskey Cask).
If you can't narrow down your beer style even to the general category of, say, Porter, then I'd suggest possibly entering it under Specialty (Category 23). In order for a judge to really be able to evaluate your beer, you have to be able to give him or her some indication of what you were going for. Even in Specialty, you have to be able to describe it well enough for it to be fairly evaluated (what type of special ingredients or processes were used, etc.). Narrowing it down to the general category (i.e. Porter) and entering it as a Wood Aged Beer should be able to be done, though, couldn't it?