Oblivion is the retail version and the DLCs were a direct download from BethSoft (or whatever their online store is called). Apparently from trawling t'Internet, the direct DLC is not compatible with 64-bit (if I'd bought the retail DVD DLC collection it would have been compatible it seems).
Allegedly, should be possible to get a refund and then buy the retail version which is compatible, but to be honest for a 5-year old game I'm not sure it's worth doing - it's not like I play it that regularly these days