There are two ways multiple tasks can be moved on the Timeline at the same time.
The first is by selecting the tasks you want moved on the timeline. To do so, press and hold CTRL and click on each of the desired tasks.
Selected tasks will be highlighted in green. To then move them, contionue holding CTRL, click on one of the selected tasks and drag them to the new position in the timeline.
The second, is moving depandant tasks. Hold SHIFT + CTRL and select a task. Once you click on the task, that task and all related tasks that follow will be selected.
Drag and move all the tasks to their new time frame.