If it is going to be realistic(ish), like Angry Birds, then for each object that is blown apart by the bomb, it will follow a quadratic path.
I dont know andengine or box2d. But I have done simple 2d explosion and projectile modelling in a game.
I hope you can take something from the following:
You would want to find out the (x,y) coord distance of the object from the bomb. From this calculate the angle. (for example an object above the bomb as it explodes will have angle 90 or pi/2.
From this work out the sin and cos of the angle. Multiply it by some force factor F. (depend son the strength of the bomb and distance of object from bomb.) From this you have your initial vector of movement {F*Math.cos(angle),F*Math.sin(angle)};
From here out it is just plane kinematics. The object should follow a quadratic path through the air. The equations may look something like:
object.setXCoord(object.getXCoord()+time_constant); //after initial explosion, no force is
//acting horizontally on object.
object.setYCoord(object.getYCoord()-some_constant*time_constant+another_constant*time_constant*time_constant);// note Y's path
//relative to time is quardatic.
You will probably need to add some casts in there depending on what types you will use. All the constants depend on your game. time_constant may well be 1, but I found doing a multiple of 1 made the explosion more visually appealing. i.e. as your time counter t increments, the movement of the object may use time_constant 0.5. I used a lot of trial and error to see what constant values worked best.