That is normal behavior for your multiple self tion case. Visio thinks you're trying to move the entire connectors.
In not at my computer so I can't say with certainty, but something like this ought to work... With the pencil tool selected, move it over a connector and a blue point should appear. If so, go find a point on the connector and click select it. From hence forth, hold down the shift key and click select each point you want to move. You ought to be able to continue the process for each additional connector. After all nodes selected, press the left mouse key and drag these segments to where you'd like.
An alternative scheme would be to use the association selection tool to grab the points you want.
HTH