1. He probably didn't see you. He usually walks around completely oblivious.
2. She strolled through the park without an umbrella as if oblivious to the rain.
3. He was studying for an exam on the train and was oblivious to the police activity at the other end of the car.
4. She can't stand people who walk around completely oblivious to what's going on around them.
5. I was daydreaming in class and was oblivious to the fact that it was my turn to speak.
Oblivious means being unaware of things going on around you.