Currently, dunno if it was working before or not - Weapon Training - Thrown - Does not apply it's bonus to Throwing Axes, while Weapon Training: Axe - DOES apply its bonus.

Why is this odd? Weapon Training:Two Handed - from Two Handed Warrior, and Weapon Training: Heavy Blades stack with each other normally when using anything from the category of both Heavy Blades and Two Handed melee weapons.

This is as of 2.0.6l update. Unless it just bugged out for me, secondary confirmation be needed. Personally tested it across three different characters.

Ok, I could not find any information on this other than a galore of posts on the p&p game which are useless.
These things are...weird.

They do NOT count as melee weapons, you cannot apply lead blades for example.
They are also NOT melee attacks and thus do not benefit from things like power attack. Oddly enough though, you can attempt cleaves, but the attack will simply dissipate and not do anything.
........UNLESS you are offhanding a melee weapon.
Now you can cleave at 30 feet range with the offhand melee weapon. and this will trigger the advanced cleave feats (though those will will work correctly in actual melee range).
And this is a regular melee attack, so lead blades, power attack etc all apply.

The throwing axes DO count as ranged weapons though so the ranged feats work on them, but not the bow specific feats.
And you would think it obvious that they are NOT bows, so anything that buffs bows is out.
....Except you can then apply ammunition to throwing axes ? so uh...I guess you just throw the entire quiver at people?
Oh and get this...if you have your melee offhand? well now the ammo apples to your melee attacks too.
And the cherry on top? They are not consumed. So you have infinite midnight bolts!