shake: The most general one. to move up and down or back and forth. It refers to persons or things.

(发抖) quiver: To tremble a little. It suggests a rapid but invisible vibration.
His lips quivered with emotion.

(颤抖) tremble: To shake uncontrollably and slightly as from fear, cold, excitement etc. It implies uneasiness and nervousness.
Her voice trembled as she began to sing.

(瞬间发抖) shiver: To tremble from fear or cold. It suggests a slight and rapid movement.
He stood shivering in the snow.

(极度颤动) quake: to shake or tremble violently. It suggests a more violent and sudden change. He quaked with excitement.
An explosion cam make the ground quake.

(抽筋般颤动) shudder: To shake uncontrollably for a movement. It suggests a more intense shaking.
She shuddered at the sight of a snake.