Dash: moving in a hurry, probably because the person is in a hurry or needs to do something urgently.
I dashed to the shop before it closed.
Dart: suddenly moving quickly.
I saw a man darting behind the bushes.
Stride: walking quickly with big steps, appearing to have a purpose.
She strode up to his desk, picked up the paper and tore it to pieces.
Pace: repeatedly walk to one direction and then back again, usually indicating that the person is worrying or is anxious.
The nervous father-to-be paced up and down the corridor, waiting for the doctor to call.
If someone charges into/around/up/down, they are moving quickly, without care.
He charged into the crowd and tried to stop the men by holding their arms back.
March: moving quickly, angrily, with a purpose.
He marched into the room and accused her of lying to him.
Storm: moving (usually getting in or out) quickly.
Fuming at his wife, he stormed out of the house, without bothering to listen to her side of the story.