Your needs here are rather different from those of the Question cited by Qmechanic (although the Answers there are certainly relevant). One nonspecific freeware possibility might be Google Sketchup, but perhaps you should decide whether you're willing to pay for the home edition of Mathematica, which would certainly do what you need, and many other things that would be relevant to olympiads, etc.
EDIT: Note that students don't need Mathematica to interact with any Mathematica Apps you construct, they can use a free player such as http://www.wolfram.com/cdf-player/
Non-interactive diagrams are now much less often printed out on paper, particularly by students, so that there is progressively less need for diagrams to be static. You might be better to think of ways to construct interactive apps (for which Mathematica is one possibility, Sketchup less so).
I look forward to seeing what other suggestions might turn up here.