The answer to my question is Solly Hofman of the Buffalo BufFeds in the old Federal League in 1915. Hofman started all infield and outfield positions (several other BufFeds started at least six different positions that year). He also started a game when longtime catcher Nick Allen's gear broke just before the game. He caught one batter, who flied out to right field and then moved to the outfield as Allen came into the game. On another day, when pitcher Russ Ford's pants split during the pre-game warmup, Hofman was sent to the mound. He pitched two balls to the first batter and then moved to the outfield as Ford, safety pins holding his pants together, replaced him.
Easier questions: Name the major league player since 1950 who has over 350 homers and a winning record as a pitcher.