I can't say too much about Karma, I played her once and did not like her what so ever. I don't see Karma doing anything special that other champs don't do a lot better.
As much as I like Kayle, she gets outclassed by many other champs. On paper Kayle has a lot of utility, she really is a jack of all trades. She has up to 15% reduction on an enemy's armor and magic resistances, a ranged slow, a heal and movement speed buff rolled into one, near constant ranged AoE for some pretty good harass while farming at the same time, and a 3 second god mode buff. The problem is that there are better champs that do one or two of those things a lot better while doing a lot more damage or being a lot more tanky and you can cover all of those bases with 3-5 champs that all singularly perform better. I'd rather have a Soraka healing. Sion has a ranged stun, Ryze has a ranged root, and many champs have slows. Many champs have AoEs and AoEs are situational. God mode... I don't think anyone has that where they can place it on someone. Tryn's got god mode but only for himself. All of these champs save for Soraka out-damage Kayle by leaps and bounds, and Soraka's got far more healing output(on top of reliable AoE).
Master Yi I don't really get, I've seen many good Yis and many bad Yis. Who's more favored in the melee DPS category? He's got good abilities. Alpha Strike is silly in terms of harassment, in the same category as Fiddle's crow but a bit less since Yi potentially puts himself in danger every time he does it. He's got a regeneration ability, and a massive speed boost & immunity to slows. The only thing I can think of is that he's got no CC at all unless you grab a Frozen Mallet or something.
I can't say too much about Sejuani, she seems really odd. Her CC ability is through the roof but besides that she just kind of runs around in a team fight with not much to do once the CC's out.
Twitch... eh. As ranged stealth he can get you pretty good and his ult just hurts when caught in a bad spot. Like all champs based on stealth though, you're totally crippled by oracles and pink wards.
Viktor I enjoyed playing quite a bit but he takes too long to really get going. I actually like his CC... if a slow is all you need then hey, it's there. I think many people ignore the concept of using his CC on an already slowed target to get the stun. Combine him with Galio's ult and you can get a good number of stuns in. Use Viktor's CC to place just ahead of someone running away from Nunu's ult to force them to detour and potentially take the hit because they won't make it out in time or to take the slow and stun in the hopes that they make it out. Combine him with a real good Tibbers stun and keep them there for longer and potentially get a second stun going. He's got good nuke potential when his ult is available but his damage output isn't there without it. I think he's a victim of being too situational.
Volibear I don't understand at all, is it just an outcome of a better pick? I'm not too familiar with him and things like scaling but he doesn't sound like a bad offtank at all.