It's really tough to beat an OD 1v1 in mid lane but you can deal with him in the same way as you would a Viper or a Shadow Demon.
Basically you need to ask for ganks.
However, don't lose faith, here are some other tactics I've learned that work on him.
1. The mana drain thing is a double edged sword. Sure it's ridiculously stupid when you're down to 13 mana and can't do jack crap, but because of the way Dota works, you will regain mana based on the % amount of mana you currently have when the int is returned to you. This means that you can actually OOM yourself, use a tiny bit of mana regen to regen your 13 mana pool, wait for the thing to wear off and get 100% mana back.
In other words, just spam your spells on him. After all you can get the mana back for free.
It takes a little practice to know when to use spells and when to wait, but in time you'll get it.
2. A soul ring will give you bonus mana when you use it, so it's independent of the mana that OD steals from you.
3. If you're someone like say... Sniper or Lone Druid who has very long range, just right click him. If you want you can even give up getting last hits as it's probably more important to you to get the blasted motherfucker out of the lane. Right click him until he runs away like a little baby girl.
4. If you're someone ultra tanky at level 1 like Ursa or SB, just kill him. Grab a stout shield, some stats and lots of regen and punch him to death. OD is so squishy it's kinda silly. And if he imprisons you he can't save himself.
5. There happens to be this one hero that uses almost no mana, has a ranged attack and an orb (that uses no mana) that hurts like an unbelievable bitch, and is almost immune to magic damage.