If you look in \Data\Sound\Voice\PCSoundsomename.esp, you will find a bunch of folders. Create a folder with the race's name (I'm not sure in your case, maybe "Ohmes"?), and copy the contents from one of those other folders into your new folder.
Yeah, I figured it out - there are folders for all the races (argonian, elf, dremora, imperial, redguard, nord); I only had Imperial in there, so of course it would only work for Imperials. I changed the folder name to High Elf on a hunch (Ohmes are referred to as Bosmer in game) and it worked!

The option voice set http://theelderscrolls.info/?go=dfile&fileid=432, should give the Ohmes Raht voices in game, and make them at least yelp and scream in combat.
You may need to use the CS to modify the voice used for your character, this may interfere with the voice set I linked to. I use the sound sets made by brucevayne, but I have not played an Ohmes Raht yet.
I use brucevayne's sound sets too. Your link gave me a 404 error, though.