Moving vectors to specified coordinates in QGIS?

Yep sure can. Like alexgleith said you can use the qgsaffine plugin (from the plugin installer)

The top of the first line is at 0,0 and the top of the second line is at 5,5. At the start the points are along 0 on the X.

Using the Affine plugin we can add 5 to all the X coordinates:

Then after they are all on the second line at X 5, Y 5:

If you want to move them manually, simply start editing, select the features you want to move and then select the move tool and shift them.

To move them by a particular x,y offset, you might be able to use the python plugin "qgsaffine".

I am not up to date with using the python console, but there is probably a solution there too.

The plugin in the accepted answer is not available anymore. The Affine Transformations is available and is very useful.

With this plugin you can create a formula. In the screenshot I shifted all cells with 17.396 (meters) to the north.