The When Revealed ability of The Stranger will do nothing if one or more players cannot choose an eligible character. In other words, it will only work if both players have at least one character in play in a joust game, or if at least two players have a character in play in a melee game.
Each character with the same printed cost as any of the chosen characters will only be killed once (including the chosen characters themselves), even if two characters with the same printed cost were chosen. All characters are killed simultaneously.
A player is allowed to choose a character that has already been chosen by another player. The chosen characters are referential targets, so you are allowed to choose a character that cannot leave play or be killed.