Thanks to all the responses from people who listened to the short audio I posted the other day of a man "speaking strange Vietnamese".  I got all kinds of answers from "it's Vietnamese" to "it sounds like Thai mixed with Vietnamese" to "it sounds like a Thai or Cambodian man speaking Vietnamese".  Some people actually understood the content quite clearly, which talks about Jesus, while others couldn't understand it at all.

In fact, the segment was neither a man speaking Vietnamese nor a foreigner speaking Vietnamese with an accent.  This man was speaking his native language, which is Mường, a language closely related to Vietnamese, and perhaps closer to the origins of the Vietnamese language.  The Mường people are basically ethnically Vietnamese but live in the mountainous areas of North-Central provinces such as Hoa Binh and Thanh Hoa.

Although considered a separate language from Vietnamese, many Vietnamese speakers will find they can understand much of the Mường language without studying it.