Seeing how Stromkern is making (partially) Electro music, the literal translation "Power Core" seems obvious.
While almost any word has context-sensitive meanings, I wouldn't say either Strom or Kern is highly context-sensitive, they both have a well-understood and invariant basic meaning.
Strom is always something that's somehow flowing rapidly or with great force, like electrical power, a large river, or a mass of people.
Kern is always the center/most important part of something that can be differentiated from the rest, be it a physical object (like "the inner core of the Earth") or something immaterial (the core statement of this text is...).
I would say that both Strom and Kern need context to give them their final meaning, but their general meaning, the idea that they are transporting, is quite fixed on their own.