You originally mention trying to heat with a 'fireplace' - so that is definitely a loosing proposition. Then you mention heating with 'too small' a stove 'vented into' the fireplace (no insulated flue liner, I suppose?). So that would be marginal as well, and nearly as bad as the fireplace at worst.
The efficiency difference with an OAK is going to be minimal at best. Yes, you are bringing in outside air, but that outside air is cold, so the firebox will be a tiny bit colder as well. If you burn 'warm' indoor air, yes you are using some of your heated air, but the firebox is also a tiny bit hotter,too. OAK is mainly for very 'tight' houses where a stove might struggle to get enough air.
Sounds like in your case, the 'right size' stove, burning dry wood, or pellets and operated in an efficient manner, with a fully lined/insulated flue would get you a long way toward your goal of efficient wood heat. Then, if you need to squeeze 1% more heat out of the set-up, you could consider an OAK.