Preheat oven to 375F degrees. Line two large baking sheets with parchment paper.
On work surface, roll puff pastry sheet dough out to 14x11-inch rectangle. Cut vertically to make two 11x7-inch rectangles. Cut crosswise into total of 44 strips (7"x 1/2-inch) for the sausage links. Pat sausages dry with paper towels. Wrap 1 strip of dough around each sausage. Press firmly at each end to secure. Place on baking sheets 2 inches apart for even browning.
Bake for 15 to 20 minutes or until golden brown. Meanwhile in small bowl, mix mustard and oregano. Serve sausages warm with mustard sauce for dipping.