These nouns refer to a prevailing or preferred manner of dress, adornment, behavior, or way of life at a given time. Fashion, the broadest term, usually refers to what accords with conventions adopted by polite society or by any culture or subculture: a time when long hair was the fashion.
Style is sometimes used interchangeably with fashion, but like mode often stresses adherence to standards of elegance: traveling in style; miniskirts that were the mode in the late sixties.
Vogue is applied to fashion that prevails widely and often suggests enthusiastic but short-lived acceptance: a video game that was in vogue a few years ago