I've seen this kind of thing attempted before. I'd recommend talking to the folks at the You Make the Card forums on the WotC web site. I used to be very active there, and they're a good crowd with a good sense of what works.
My general recommendations are to not try to represent too much of the champion on a given card. You're not trying to render their kit on a magic card, you're trying to capture their essence. Think carefully about what colors you assign to each champion, and try to square that with not just their personality, but what they do. Every color should be justified in both card mechanics and champion personality.
I looked up your cards on Cardsmith, and they are a little raw. Card by card.
Amumu: Green is definitely the right color for him personality-wise, as someone who seeks community and friends. But your mechanics are kind of iffy. Intimidate and undying are both unnecessary on him, and green does not get direct damage like that at all. Mechanically, you've made a black card, but Amumu isn't black, so you costed it with green mana instead. I'd keep the green, and focus instead on Amumu's binding nature. Possibly "~ must be blocked each turn if able"?
Ahri: She's not really white, and neither is this card. If anything, she's migrating towards green. As it stands, Hexproof is just weird here. It's not really a white or red mechanic, and it's downright oppressive on a pinger. Anyhow, Ahri isn't so much resistant to spells in game as she is dodgy. Self-bounce is a much better expression of that, I think, and perfectly red. Perhaps tie that to the pinging to make it a bit more of a tradeoff?
Alistar: No reason for him to have trample by default rather than be granted it by the ability. This isn't bad, but it feels underwhelming. There's little defensive focus beyond not being able to attack; he's just a bundle of stats.
Akali: This one is pretty awkwardly designed. It's not really on color or on flavor. Ninjas aren't green, they don't get stronger the more of them you have (the opposite, really), and green doesn't get double strike or lifelink. Why Akali's green I'm also unsure on. Sure, she likes balance, but that's not exactly a green-exclusive attitude, especially considering ninjaing is her method of preserving said balance.
Aatrox: He's certainly red, though I'm not sure if he's RB rather than mono-R or RW. Mechanically, however, this card is pretty much monoblack. And I don't think it quite captures the way Aatrox puts an emphasis on fighting.
If you don't mind, I'd like to take a crack at redesigning these.
Amumu 3BG
Legendary Creature — Zombie
Deathtouch
Amumu must be blocked each turn if able.
1/4
.
Ahri 2RR
Legendary Creature — Human Fox
Haste, first strike
R, T: Deal one damage to target creature or player, then return Ahri to its owner's hand.
3/1
.
Alistar 4RW
Legendary Creature — Minotaur Warrior
Whenever Alistar deals combat damage to a creature, put a command counter on that creature.
RW: Remove a command counter from target creature. If you do, you control how that creature attacks and blocks this turn.
2/7
.
Akali 2UU
Legendary Creature — Human Ninja
Ninjutsu 3UU
Whenever Akali deals combat damage to a player, put a shadow counter on it.
Remove a shadow counter from Akali: Akali gains hexproof and can't be blocked this turn.
4/1
.
Aatrox 3WBR
Legendary Creature — Warrior
Flying
At the beginning of your upkeep, put a -1/-1 counter on each creature.
Whenever an attacking creature dies, its controller may pay three life. If he or she does, return that creature to the battlefield under its owner's control.
6/6
