From Wikipedia, a portrait is an artistic representation of a person (or persons) in which the face and its expression are predominant. How you make it unconventional is up to you.
That is the definition I have given for the President’s Trophy, and gives one a great deal of latitude for interpretation and creativity.
If you Google Unconventional Portrait Images you will find many examples of unconventional portraits that may help. Also I will be presenting some images on our Share Night on 25th September that may assist you.
I have also found on Lynda.com which, as I have mentioned previously, can be accessed through the State Library of Queensland, an interesting course by Paul Taggart named Story Telling Through Unconventional Portraiture. This is well worthwhile viewing as it will give many ideas on photography and portraiture.
I hope you have lots of fun, and come up with some interesting ideas, and I look forward to having many unconventional portraits to judge.