mh, looks like you got a problem with openal, part of the lightweight java game library afaik (lwjgl)
try downloading the files again by deleting them (.techniclauncher/tekkit/bin/natives and starting tekkit again.
if that does not work, download the latest lwjgl-files and put them in the proper folder (jars to .../bin and .so-files to .../bin/native)
doesn't work? dunno. maybe someone else helps