Small story- short story- this is the natural name, but this isn't a story, so say 'in this article/piece'
How about- If you look at the results of the Canadian national team
you will have no doubt that it was the Canadians who invented ice hockey (...all your doubts about whether it was the Canadians who invented hockey will be dispelled.) I'd use the second here.
an odds-on favourite - the odds-on favourite
Since then the Canadian team has stopped
an overwhelming favourite- the overwhelming favourite
The Soviet hegemony had lasted up - The Soviet hegemony lasted up
Due to the lock-out in NHL Russian hockey- Due to the lock-out in NHL, Russian hockey