Almost every champion in League of legends can play every role.
BUT they are not viable in all those roles.
What can Leona do?
Leona is GREAT for tank and GREAT Support roles. You can make a huge difference in the game if you are playing one of those two roles as Leona.
Can she Jungle or AP Carry?
Yes she can. But she shouldn't be doing it.
I'll not make too much enforce in showing you the right way to do the Jungle or the AP. But here some information any way =)
How to Jungle as Leona (This is a little out of date, but gives you the general idea)
Compilation of AP Leona
But why this is not a good idea?
She does an amazing damage? YES She does, and if you play Leona as an AP, she will wreak havoc, if you play her as jungle you will clear and gank really fine, even as an AD carry Leona. But, she is not mastered this way, because she loses for others AP like Annie and Brand for example. so is better you play AP Brand, and play Support/Tank Leona for real and play for fun AP Leona.
Here good guide for tank leona e for support leona.