The Beta Stromgren system was an uninhabited star system in Sector 25434. The system was in space claimed by the Romulan Star Empire.

A Federation long-range unmanned probe, Vega Nine probe, had charted this system, which lay twenty-three parsecs beyond the limits of manned exploration at the time. This system was destroyed in 2366 when its primary, Beta Stromgren, became a supernova. (TNG: "Tin Man")

"STRUM-gren" was the pronunciation for the system's name from the script pronunciation guide. [1]
According to Star Trek: Star Charts ("United Federation of Planets II") and, the Beta Stromgren system was located in the Beta Quadrant.
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