I would suggest
eclectic from Oxford living dictionaries
deriving ideas, style, or taste from a broad and diverse range of sources.
"her musical tastes are eclectic"
synonyms: wide-ranging, broad-based, extensive, comprehensive, encyclopedic;
of, denoting, or belonging to a class of ancient philosophers who did not belong to or found any recognized school of thought but selected such doctrines as they wished from various schools.
a person who derives ideas, style, or taste from a broad and diverse range of sources.
While the dictionary definition seems spot on, to my ear I would still single out "interests" or "knowledge" or "tastes" - Man of eclectic interests. Home decorated with an eclectic variety of styles.
For your sentence I might say:
Ken Jennings is a
very _______ man a man with eclectic knowledge. He won 74 editions of the Jeopardy! Game Show.
the definition above suggests "encyclopedic" as a synonym, which could be another fine answer however I do not think that quite emphasizes the ephemeral nature of Jeopardy trivia.
Jeopardy might have a category "Adele song titles" and a clue like "like a cannonball that fell off a ship" and an answer "what is 'Rolling in the Deep'
Things like the names of popular song titles are learned from living, not study, and I think the word eclectic, which emphasizes variety of sources and their natures works well.