I think you have the magnet button on, as on the display below, this means that objects that are tracked together (those stacked on top of each other) will move together, if you turn the magnet off you should be able to move the objects independently of each other.

On the toolbar, just above the tracks in timeline mode there are the icons for group/ungroup

Now, you need to click on the object, lets say it was a video with audio, when you click on either the video or the audio part of that clip they both highlight... this means they are grouped, so if you wanted to delete the audio or the video you but leave the other part, then you would need to press the ungroup button as they are highlighted. This will ungroup them so you can delete the part or move the part that you want.