Writing in tongues

On August 12, 2011, Caitlyn wrote, ....My story is set in modern times, but it has a group of major characters who have been around for a few thousand years, and English is not their first language. Though they speak English around the MC, in stressful or emotional situations they revert to their native tongue. Many of those lines of dialogue are left uninterpreted, at least for a while.
    I feel like the language needs to be included for authenticity's sake, so I was wondering: what is the ...