That is strange. Have you verified the presence of the following in your skyrim\data folder:
Skyrim - Animations.bsa, Skyrim - Meshes.bsa, Skyrim - Sounds.bsa, Skyrim - Voices.bsa, Skyrim - Voicesixtra.bsa
If they exist, verify you have a section for them in your Skyrim.ini similar to:
[Archive]
sResourceArchiveList=Skyrim - Misc.bsa, Skyrim - Shaders.bsa, Skyrim - Textures.bsa, Skyrim - Interface.bsa, Skyrim - Animations.bsa, Skyrim - Meshes.bsa, Skyrim - Sounds.bsa
sResourceArchiveList2=Skyrim - Voices.bsa, Skyrim - Voicesixtra.bsa
Barring all of that, you may try deleting those ^^^ .BSA files, then verifying game cache via Steam to redownload them.
They exist, I've checked to make sure the *.ini files (all of them) say to load/archive them. And, unless I'm horribly mistaken, Steam's game servers verify from the same place you download from. Remember when I said I'd reinstalled after manually deleting them? Would that not have done the same thing ( I think so, but if you have better info, plz share

)?
Check your Steam language settings. Are you sure you have English selected? This will affect what speech files the game downloads.
Since all of my games are in English... wouldn't that setting affect my other games?
Also, check your audio cards speaker/surround sound setup. Maybe the game is trying to play the speech though an un-connected/ non-existent speaker. Try setting it 2-channel stereo.
Where would I find this in my game? Truthfully I don't think this is it though; Heimskir (Talos shouter in Whiterun) has been missing since glitch began.
One last thing I thought of, is if you have too many .BSA files loaded in skyrim.ini under the [Archive] section, it will cause problems because of the 255 char limit. Note, this is only applicable if you have modified that section and added .BSA files (DLC, fixes)
To alleviate that download and install [link]
I will try this, but given that the Talos shouter in Whiterun is missing, I'm not sure if this will help. But it's worth a shot!
Any other ideas?