This British idiom means unable to hear anything at all. Does "post" here mean a piece of wood? Thank you.

Yes. A post is a piece of wood (although nowadays it might be made of other materials). It's not just any piece of wood, though. It's much longer than it is wide and it's driven into the ground to serve as a support for something else, for example the cross beams of a fence. You'll also hear "fence post". Emotion: smile
Thank you CalifJimEmotion: smile