I am convinced that Mordekaiser needs a nerf. He beat me regardless of my attempts at mid. That was some of my best playing too.
Are there any counter-Mord strategies I could employ?
A lot of people under estimate Morde at mid. Huehuehue
Anyway, as someone who pretty much mains Morde, I can tell you his number 1 weakness is speed. A morde under a tower is pretty much ungankable as he can just wipe the minions under the tower, then proceed to smash you with the turret as backup. You're best bet is to let him push more and give up some last hits if you have to. Having him at your tower makes him super easy to gank as he has no CC and will usually only have flash, plus he's slow as balls. Also, the earlier you can gank him, the better.
Final tip, don't stand next to your minions ever. His cone blast thing becomes twice as effective in that case. Stand far enough to the side that he has to chose between hitting minions or harassing you. Once he commits, you've got about 4 seconds to hit him as much as possible. You should easily drop his shield at earlier level, so when that happens, try to do as much damage as possible. Having Morde go back to base is one of the best things you can do as it takes forever for him to get back in lane.