I managed to win a tournament with this deck.
Against aggressive opponents the main strategy is to play a fairly slow game. Put down your deeds, start to equip your dudes and wait for the opportunity to strike hard. The deck has a fairly strong shooting structure so you don't have to fear too much, especially with Tommy Harden on board and Pistol Whip, Unprepared at hand. At the second part of the game you can bring in Judge Harry Somerset or Clyde Owens and start to hunt down wanted dudes by force.
Against weak shooting decks, like landslide you can play offensively right from the start. Occupy the town square, grow your economy with Recruitment Drive and A Coach Comes to Town, put bounty on key dudes and bring in one of the above mentioned executioners as fast as you are able.
Small trick: if you have Undertaker under your control, you can ace one of the multiple dudes' card who is already on the board with Gomorra Parish. This way you get rid of an unusable card from your hand and get 3 GRs in the process.