You can click on a label and manually move it, but that's dangerous and will usually fall apart. Various changes to your data will wipe it out, etc.
The better approach might be to remove the labels altogether. With a visual representation of this data, the labels just add unnecessary clutter. Remove them and allow people to get more detailed info via the tooltips.
If you absolutely must have labels, then what about using a small multiple chart? Drag Measure Names to the Rows shelf and that will create three separate charts, one for each measure. This is a great way to show overlapping data like in your line chart.