Are the actual official Japanese words for sexual harassment and power harassment... just Japanese pronunciations / abbreviations of the English terms?
Yes. In Japanese this kind of abbreviation does not carry the childish/frivolous connotations it does in English.
In my experience, the connotations are very similar to English use. What matters is the context. Say sekuhara or sexual harassment at work: very serious connotation. Amongst friends or in media (comdey/anime/etc): potentially frivolous/unserious connotation.
It's very different IME. A catchy abbreviation of a serious subject would almost always be inappropriate in English-speaking spheres, especially in a business setting.