They enable you to choose the degree of spread of your pattern. An "open" choke, like improved cylinder or skeet, will give you lots of spread - this is good for short range work, since it's more forgiving of aiming error, plus the shot won't be so concentrated, so it won't mangle a small bird you were planning on eating. Toward the other end, the full or extra full choke keeps the shot in a tighter group, so it's more concentrated downrange. This might be useful for larger birds and/or longer ranges.
Shorter barrels do have more inherent spread than a longer barrel with the same choke, but there's a lot of overlap in their pattern size. I'm guessing here, but your short barrel might give you one step more spread than a long one (a full choke in yours might pattern like a modified choke in the longer).
You should consider taking some large (30x30") sheets of blank paper, like butcher paper, and shoot them with the different chokes at different ranges. This will give you an idea of the size of the pattern for different conditions, and also show you where the center of the pattern is hitting relative to your point of aim.
*zipping up fireproof longjohns for the inevitable flames*