First, join the ODD support group on Facebook. It's very active and full of first-hand insights.
We've been dealing with ODD for many years. The only words I can think to describe it would likely get me banned here for profanity. Let's just say it's awful. We have had some success, though, with medications like Risperdal and Abilify. Our son went on Risperdal for an eating disorder and it eliminated the ODD. He had a bad reaction to it, though, and had to switch to Abilify. Currently, the dosage isn't quite right and the ODD is back. Hoping to get that fixed when we get in with the psychiatrist next month.
Basically, your child just wants to irritate you, teachers or anyone else targeted. People with it will deliberately cause chaos and are stubborn to the 1,000,000th degree. Our son has ADHD-combined type, too, and I can say this combination makes life very, very difficult. It can be hard to tell where one condition ends and the other begins. I've had to deal with him refusing to go to school (and being 100 lbs., too heavy for me to haul to the car), objects thrown at my head for crazy requests like "Hey, it's time to do homework," having to lock myself, daughter and dog in our master bedroom to escape him.
I wish I had words of hope for you, but instead I just send hugs. You're not alone.