Hey there again B33TL3, I have played and own all of those champions. They are all ways fun and unique in their own ways.
As shen I went a whole game in the jungle and only let 1 person die the whole match
As Akali we were close to losing, the enemy jax had been fed enough so that no one could kill him. Well untill I got invloved anyways, they had all 3 inhibs destoryed and baron but because of akali's AoE skills and her natural auto damage I got enough gold to get madreds as my final item and win the match. While her passive doesn't do damage to turret it still damages the inhibs and nexus lol
As teemo, hes the only true "scout" His mushrooms are easy to place, but hard to master in terms of placement. No great story but a delite all the same
As for Kat shes fun for her mid game strength, if you play her well there you can carry your team to victory. Also one of the few champs that can do AD or AP on an even level.