Today the British weather is living up to its reputation: raining ? - it's chucking it down ... So, being stuck in the house when I should be 'out there' with the bees, I thought I'd try and answer your question: "Does Oxalic Acid kill tracheal mites ?"
The short answer is - it probably COULD - but only under certain circumstances.
The much longer answer involves some biology and some chemistry: the biology relates to understanding the mode of entry of the tracheal mite.
The honey bee trachea is connected to the outside world by ten pairs of smaller diameter spiracles, and the pair of interest are the first of these which are hidden beneath the spiracle lobes, a large hair-fringed backward extension of the first thoracic segment. These are the spiracles which are invaded by tracheal mites.
Now the hairs seen in the picture above serve an important function - they prevent the bee from inhaling airborne dust of around 30 microns or larger, which brings us to the chemistry of Oxalic Acid.
Oxalic Acid exists in two forms: anhydrous Oxalic Acid (which I'll simply call OA) and Oxalic Acid Dihydrate (OA-D). The Dihydrate is the stable form, and the form most readily available. If a container of anhydrous (laboratory) OA were to be left open for any length of time, then OA-D would result, as moisture would be adsorbed from the atmosphere. Anyone who has used OA-D knows it to be a rather 'damp' material, with the crystals being prone to clumping together.
During the vapourisation process, water is initially driven off, with anhydrous OA vapour resulting, only for that emitted vapour to very quickly adsorb moisture again from the atmosphere, with a cloud of airborne OA-D dust resulting.
Now - if this dust had a particle size significantly less that 30 microns, then it could be 'inhaled' by the bee, would contact any mites present, and duly act as a miticide. So whether OA-D is an effective honey bee miticide or not depends upon it's particle size.
So - what size are the OA-D particles created by vapourisation ? No-one can ever determine this - because the resulting particle size depends upon the temperature and humidity at the moment the vapourisation takes place, as temperature and humidity combine to determine the amount of water which is available within the atmosphere to enable OA to revert to it's stable OA-D form.
Therefore on cold, dry days there is a greater chance (and I wouldn't put it any stronger than that) that OA-D particle size might be sub-30 microns, and thus able to to access the honey bee trachea and act as a miticide. On warm, humid days it certainly wouldn't.
Although this explanation doesn't answer your question, I hope it helps you to understand the issue - which unfortunately isn't a clear-cut one of being either "Yes or No".