Getting a job in industrial math with only a Masters? Is it possible to get a job in industrial mathematics with a Masters in math but no work experience and no PhD. Or would one be limited to only nonresearch industrial math jobs?

How about the type of jobs listed here: http://www.siam.org/careers/thinking/solve.php
?
Students with master's degrees an applied mathematics (and statistics, OR, actuarial science, mathematical finance, etc.) often find work in industry doing applied mathematics, but this work is not typically "research" of the sort that results in publications in research journals.   If you want to do publishable research, then complete a PhD.