I think you will have a hard time trying to find something that tells a story that isn't country, but I'm browsing my music library as I answer so bear with me....
Ok, here's what I can think of:
Country
Strawberry Wine - Deanna Carter
Farmer's Daughter - Rodney Atkins
Three Wooden Crosses - Randy Travis (A REALLY good one I think for your assignment. If you need more clarification on what the song means, please let me know)
Bullets in the Gun - Toby Keith
The Little Girl - John Michael Montgomery (another really good one I think)
Believe - Brooks & Dunn
Sara Beth (Don't remember who sings it)
Earl had to Die - Dixie Chicks (I think)
Traveling Soldier - Dixie Chicks (That one always makes me teary eyed lol, and another good one for your assignment I think)
How do You Like Me Now? - Toby Keith (I think)
Pop
Skater Boy - Avril Lavigne
......that's the only one I can find that I have, although I'm sure there are more pop songs that tell stories...
Rock
Not Good Enough for Truth in Cliche - Escape the Fate (you can't tell as well from the actual song, but the music vid tells the story with it. You might have to work to sell it though as telling a story :P)
No One Really Saw Her - Hinder (I don't think that's the real title though...but that what it is in my media player)
Lucy - Skillet
I'm sure there are more out there, but honestly it seems most Rock songs that tell a story like that are more....veiled in their lyrics for lack of a better word. The country songs I listed are going to be your best bet I'm sure. The ones I listed are pretty straight forward and easy to get the story behind them.
Good Luck!