Q: will calisthenics or excercise help burn the extra calories of eating a heavy meal?

A: Calisthenics are a very effective form of exercise, but it's really not a healthy or a productive approach to think in terms of overeating in any one meal and then burning it off. One heavy meal is not going to make any difference and you ought to be exercising regardless. If you have a specific goal (like to lose fat), then you should follow a complete diet and exercise program for optimum results as described here. Otherwise, just enjoy your meals, including big ones, and move on. Being physically active in general is, of course, a good idea no matter what.