I realize this question is old, but I feel compelled to add in here.
In addition to what's already been said (boost your MR, don't be afraid to over-nuke him to eat past his shield), there is the topic of range and escape abilities.
Mord is a unique melee in that his abilities have some good AOE and range to them, but he suffers the penalty of normal melee characters in that a good ranged will still be able to keep him at bay. Characters with long range and/or skill shot abilities like Anivia, Ezreal, Kog'maw or Karthus can put pressure on Mord very easily during the laning phase, which is where Mord tends to establish himself. A character with strong lane presence/harassing ability like Nasus, Garen, Vladimir or Fiddlesticks can also hurt Mord's early game by keeping him at the enemy tower where the tower will eat most of the kills.
Mord also suffers from a distinct lack of escape abilities. Ganking Mord can be easy with a properly built tank to bait his abilities into cooldown, and then bum rushing him when he has nothing left with which to counter. Slows and stuns prevent his otherwise relatively high HP and shield from making a difference, so plan ahead.
Mord tends to be very item dependent. A tank Mord ends up having lower overall damage, while a DPS Mord ends up having a very low lifepool and no escape mechanisms. Putting pressure on him in his lane early game prevents him from racking up too much money (which is why he was designed with so much AOE ability), and thus prevents him from getting his really good items at the proper time which would otherwise allow him to become the "powerhouse" that everyone fears.
Don't get me wrong, a properly played Mord is quite good, and a smart player knows how to balance between him being a tank and a burst DPS. But a heavily pressured Mord will crumble late game, and a ganked Mord will have no chance against the proper lineup.
Normally at the point you are zoned out it is too late to do much besides last hit under your tower. Because they are ranged, they can continue to harass even as you pick up those last-hits.
At that point my preferred method (without jungler help) is to back away (recall) if they are zoning me away from me turret. Buy some items and if you are not too far behind you can take the advantage. In particular and if things are very dire, buy a fortitude elixir!
I think a key point here is that against ranged champions, melee have an advantage once they get within melee range. So you really just have to pick and choose your battles and ensure you win the early exchanges as taking too much harass will just snowball the lane against you.
Remember good match ups are key so always consider that in champion select if you are running draft mode!
Best Answer
Orianna is very reliant on her ball, pick champions with high mobility and/or sustain. When playing against Orianna, take consideration of these points.
Always stay away from the ball, if you run into the ball she'll cast her spells on it. Try to dodge it too. (start with boots)
If she planted the ball near you, try to have minions between you and the ball, it reduces the damage per target hit.
Orianna's spell damage is not super high early game because of that she will try to harrass you despite her mana cost on her q being lowered a month ago or so. She will run out of mana quickly.
Orianna is very squishy, try to harrass her back, after she missed a q. you can bully her around for a few sec.
As i've mentioned before, Orianna can't instantly kill you, she counts on harrassing you to 50% health before actully attemping to attack(thats early and middle game) so if you are willing to have a clash with her, make it fast.
Orianna has such short cooldowns with the right items, not to mention that she counts on the combo of her skills all together so any silence or stun in the middle of her combo will ruin it.
Beware of her passive, it gets underestimated a lot but when she gets a few autoattacks on you, it hurts..