Oh man, this is a tough one...

Olaf because he's the only one released pre-2011?

Shyvana's DOES mention joining the League, following Jarvan.
Ahri isn't a full human (and doesn't even have a single human parent).Ahri is from Ionia.Even if you don't think Karma has boobs (she does, quite large ones actually), Shyvana DEFINITELY does.

I will say KARMA. the thematic here is based on skins: they all have skins based on either a mythical creature.

Olaf's frozen skin is based of the Frost giants menacing to bring Ragnarok onto Hasgaard

Jarvan IV and Shyvana and Talon all have a dragon skin (including normal skin on shyvana)

Ahri is based on a mythical korean creature closely related to the kitsune

the only odd one is Karma for not having a skin based on a creature: she has a skin based on the sun, culture (geisha) and her normal skin is basically empress of Ionia.

if thats not it, its a hard nut to crack

This is the correct answer.
Olaf was released in 2010.
The other five were released in 2011.

-.-

Vayne
Vayne
Vayne
Wukong
Vayne
Vayne
Vayne

Phew, got it. I picked up the hint that it wasn't lore-based, but also suspected it wasn't mechanics-based because they were just too different. So it had to be something meta.

My turn again:

Annie
Ashe
Gragas
Malphite
Sion
Urgot

Hmmm. It's not related to release dates again, is it? I see most of those were released in 2009 or early 2010, with Urgot being released in late 2010.. I don't know when LoL went out of beta and was released though. Were the other 5 Alpha/Beta champs and Urgot released after the game came out?

I kinda hope it's something different. ;p

No, that's not it... but there might be a clue there if you look hard enough.

Hm. Ashe since she's had reworks (model and skill) while the others still look/act like they do when first released? Maybe even the others' splash art hasn't changed?

I only started playing at the beginning of 2012 so I don't know older champ history that well...

is it maybe that urgot was the only one released during a season? gragas was released during the season one preseason and all the others we're released during the alpha or beta stage