Many mods have been carried over from very old versions of Warband with some even being port-overs from the original game and this is why they likely do not have the necessary code additions to unlock achievements. The option to unlock achievements is within the module system and as long as the mod uses the native code that unlocks those achievements and most importantly runs the game through Steam then they can unlock. Using mods will not prevent achievements as a rule.
Achievements get turned off if you use any mods or have cheats enabled. Achievements are disabled for the current session if you have cheats on, but if you quit the game and turn them off they are reenabled for the next load. Hmm, I've gotten achievements on a Native save after using cheats, if I quit and restart the game.
