Playing Katarina and Akali in top lane, results.
Top lane is sooooooo much easier than mid lane for both of them here's why.
In mid lane the common phrase for either of these champions is to play like a bitch until 6, the reason why is due to massive poke and high damage from the enemy mid laner so it's not like you'll be able to do much until you get your level 6 spike. This means you'll often have to deal with being behind in farm and overall gold making you roughly useless.
In top lane however it's a whole different story, the top lane for the most part is full of low damage tanks (in comparison to an assassin at least) and the vast majority are melee with little to no poke ability. This means you can farm much easier and in Katarina's case poke with your Q if they get to close, did i say ZONE POTENTIAL?! In addition all in's at level 3 and cheesy level 2 kills are infinitely easier on champions that can't out trade you until they have tank items and in many cases people will still go damage items first even if their losing.
Conclusion: Try taking Katarina and Akali up into top lane, play smart, poke and don't pick them into these champions.

Your first item will be Hextech Gunblade (regardless of match up) and your second item should be either Rylai's Crystal Scepter or one of the AP resistance items depending on which is more important.
Happy farming!
Edit: Explanation on Gunblade buy, you become a drank tank to the enemy top laner, they can't do enough damage to kill you and their not tanky enough to out sustain you either if you get this first. In addition this item has a nice 250 base damage active that can be used to either engage or secure a kill.
kind of have to go Top lane now. Her sustain was hit way to hard for mid lane and most mid lane matchups will make your life a living hell pre 6. Possibly one of the worst match ups for Akali mid might be
with her easily having 5 seeds just sitting there all lane phase. At least with top, you would have some chance to walk up to your minions and get some CS and auto attack to proc your heal. Yea there are some bad match ups for Akali in the top lane but most of them are at least melee giving you some form of safety if they push you into tower.
shouldn't even be that hard of a match up for
all that much either, if you can survive her ult then you would be fine against her imo. Though I'll agree with you on
...that is just torture to fight.