Oh dear...Oddie. I think he'd either go western or english, although I'd be dubious about what control you'd have neck reining when he decides 'no, no thanks, I'd rather go that way'. But anyway, he goes english because that's all we have.
No way would he ever be anything but a trail/hack horse, though. Don't get me wrong, he's a GREAT trail horse, one of the best, but only because he enjoys it. He does NOT move in a school and would be useless at anything requiring speed or impulsion. And before anyone says, yes, it probably is due to gaps in his training in the past and no, you couldn't make him school. Numerous people have tried, thinking they are decent trainers while we just let him get away with murder and they can fix him; they all end up sitting on a stationary horse in the middle of the arena, desperately trying to do anything at ALL to make him DO SOMETHING and being just a little humbled.
He could probably do XC - he's got a nice jump in him if you pop him over 3ft jumps on hacks - but I'd worry about whether he'd have the stamina now he's older.
Old ploddie Oddie, I love him.