Hello again!
I had no idea that we had so many pokemon fans around here! Ill go over some of the more controveral typing in more detail justification.
I think 
Ahri is Ghost/Fairy type because a) shes a spirit fox who turned into human because some dying sorcerer gave her his life essence (soul). To return human she has to take the souls of other people (she doesn't anymore) so ghost type right! b) Fairy types are attractive and lure you into a false sense of security, i.e. Ahri (Charm is also a Fairy type move).
I dont really think she's a dark type because she's not nesseacrily evil and her trickster ways seem more fairy type secduction than dark type Le Blanc deception. I also dont think she is psychic because ghost fits more accurately (her orb is asoul essence not psychic energy).
With 
Blitzcrank, in a perfect world i would go Electric/Fighting/Steel. However i think the two that fits his personality the first is Electic and fighting. Unlike orrianna he has developed some kind of emotion turning hi8m away for the coldness of steel and more of a fighting being. Also his skills are another pointer to hes typing. He really has no steel like move (well you could count Automize). The main part of his kit seems to be pull and punching people up which (seems to me) to be like fighting type moves.
Without further ado .... Part 2!!!! (hey that rhymed! XD) {() Optional typing}
Elise: Bug/ Poison (Bug/Dark): This is really difficult since you can go either way. Posion seems to be a stronger factor since she poisons the mids of others. (wait isn't that dark type tho :@ shes confusing my mind!!)
Evelynn: Dark/Ghost: a mysterious blue murderer from the shadow isles, sounds shady to me! Shadow ilse is also where all the ghosts come from.
Ezreal: Fairy: Why, because there isn't no light type, fairy will have to take over that role.
Fiddlesticks: Dark/Ghost: So mysterious this fiddlesticks is. He seems to be something from a nightmare locked up in that holding cell until the summoners need him, hence the typing.
Fiora: Normal/Fighting (Normal/Steel) (Fighting/Steel): She's seems pretty normal to be however i might prefer steel to fighting (i said might!).
Fizz: Water/ Fighting (Water/Dark): He jumps around fighting people, however I can see why you would want this trickster to the dark side.
Galio: Rock/ Psychic: Weird huh, I chose psychic because of his supportive abilites, healling, concussive blasts of psychic energy from his eyes!
Gangplank: Normal/Poison (Normal): A normal pirate with a poison blade.
Garen: Fighting/Steel (Fiighting/Normal): A wouldn't put him as normal if he can bring down a giant sword in the sky!!! However he does fight well.
Gragas: Water/Fighting (Poison/Fighting) : Do you call alchol poison or just good tasting water. I say that unless you're drowning (alcholic much) in it, small sips cant kill you. Its most likely that its the splinters form the barrel hurting you more than the grog. Just remeber water pushes, posion burns.
Graves: Normal: Most of the adcs will be normal types because they rely on their BASIC (normal) attacks. His gun is not worthy for a second typing. (mabye dark but I should stop contradicting myself :P)
Hecarim: Ghost (Ghost/Steel): We all know he's a ghost? right?
Heimerdinger: Electric (Electric/Steel): Somehow, heimy just shouts electric to me! Mabye its the turrets. :P
Irelia: Psychic/Steel (Ghost/Steel): Telekinetic control over blades, psychic much. However somepeople argue that she is more ghost since she practically undead.
Janna: Flying: Unfortunately, there is no such thing as wind types, looks like flying will have to do.
Jarvan IV: Steel/Rock (Steel/Ground): I say steel because he can summon standards. Ground or Rock whichever you prefer.
Jax: Fighting: What else is he other than an OP lampost weilding,corperal, punishment?
Jayce: Fighting/Electric: This one is pretty much self explaintory.
Jinx: Normal/Dark (Normal): Jinx? Normal? Hahaha don't make me laugh!
Karma: Psychic/Dragon (Psychic): Why dragon? Because i am bais towards Karma (my main) :P. But seriously, she is the paradogon of Ionia which two dragons floating on her back. She must have the power like a dragon.
Karthus: Ghost/Dark (Ghost): Karthus can come back from the dead. He use dark magic.
Kassadin: Psychic/Dark: He survived the metal torment of the dark void so he has the best of both worlds.
Katarina: Dark/Steel: Sinister Steel, 'nough said.
Kayle: Fire/Psychic (Fire/Flying): I say psychic because of her heal and intervention.
Kennen: Electric: Really?
Kha'Zix: Bug/Dark: He's a bug. He preys on people that are alone. He pops out of nowhere. Anything else?
For know i have to go but ill edit more in when i have the time so be sure to come back reallll soon alright. Fell free to discuss and changes or feedback thanks! (this post will be going up till quinn then ill have a third post) Here's part 1: http://leagueoflegends.wikia.com/wiki/User_blog:Leo636/Champion_Translated_into_Pokemon_types
P.S. here's Emptylord's version: http://leagueoflegends.wikia.com/wiki/User:Emptylord/Template:Pokemon
and here's Mineko Charat Lucky's version: http://leagueoflegends.wikia.com/wiki/User:Mineko_Charat_Lucky/Pokemon_Types
Edit 1: done H-K