This is going to matter on the jurisdiction, laws and how they are interpreted vary around the world. There might be issues with using Disney/Pixar/Marvel/DC characters. I would think that there would be less of an issue using something like toy soldiers, hot wheels cars, or Lego. These are more generic. If you show a pair of gloves in a course you wouldn't need permission of the manufacturer. There are actually quite a few safety videos out there using Lego (you probably shouldn't use the same characters from the Lego Movie though).
There shouldn't be a problem in using toys/characters in a challenge like this. The educational use clause usually is exclusive to public schools. I also don't think that it would be an issue using characters in a portfolio would be an issue, you're not using the characters to sell a product outright.