I have attached my final render model.
While the answer given by 10 Replies is correct - you did not have sub-surf modifiers added to the objects - I think there is another problem. The edges of the front red spherical shape, and the back rear dark shape have slight deviations. The particular angle you have chosen for your composition shows very slightly the edge of the back object.
If you have a look at the edge in Edit Mode - you will see it is not what can be considered a clean topographical mesh. Presumably by either Boolean or the knife tool you have an edge that has triangles and this is where the sub-surf will try, but not necessarily solve the problem.
You could probably get away with just adjusting the angle a bit. If you do want to fix the edge, ideally you would want an edge loop where you might add a slight bevel to soften...
Turn up the Subsurf Modifiers
If the render is too sharp, turn the render subdivisions up to 3 or 4. If the preview is too sharp, turn up the view subdivisions. Typicaly it is best practice to have lower preview subdivisions than render subdivisions.
Make sure that the object you want to modify is selected when you use the sub surf modifier.
For those of you who need more help, please watch the following gif that consists of 3 mouse clicks:
Also, make sure you do this with every single part of your model, otherwise some parts might have more creased edges.