In a 4-quart saucepan, combine sugar, water, corn syrup, and salt. Swirl the pot over the burner to dissolve the sugar completely, do not stir. Increase the heat and boil to soft-ball stage (250 degrees). Use a candy thermometer for accuracy. Wash down the inside wall of the pot with a wet pastry brush if necessary. Remove from heat, stir in the butter and vanilla.
Coat 3 sheet pans with nonstick spray. Pour the mixture onto the sheet pans, dividing in 3 equal portions. Mix the peppermint extract and a couple of drops of green food coloring in 1 batch. Mix the orange extract and a couple of drops of yellow food coloring in another batch. Leave the plain vanilla batch as is. As the candy cools, lift the edges toward the center with a metal spatula or bench scraper so they don't harden. When just cool enough to handle, butter your hands and pull the taffy into long ropes. Twist and pull until the taffy is stiff and the color is even. Cut the ropes into 1-inch pieces with clean, buttered kitchen scissors. Wrap each piece in waxed paper and store in an airtight container.
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