Code

private void OnNodeModified(object sender, NodeEventArgs e)
{
	RemoveOverlaps(e.Node);
}

void RemoveOverlaps(DiagramNode modifiedNode)
{
	var overlaps = FindOverlaps(modifiedNode);
	if (overlaps.Count > 0)
	{
		foreach (var node in diagram.Nodes)
			node.LayoutTraits[SpringLayoutTraits.Frozen] = true;

		foreach (var node in overlaps)
			node.LayoutTraits[SpringLayoutTraits.Frozen] = false;

		var springLayout = new SpringLayout();
		springLayout.SplitGraph = false;
		springLayout.Randomize = false;
		springLayout.RepulsionFactor /= 2;
		springLayout.Arrange(diagram);

		foreach (var node in diagram.Nodes)
			node.LayoutTraits.Remove(SpringLayoutTraits.Frozen);
	}
}

List<DiagramNode> FindOverlaps(DiagramNode modifiedNode)
{
	var overlaps = new List<DiagramNode>();
	foreach (var node in diagram.Nodes)
	{
		if (modifiedNode == node)
			continue;
		if (modifiedNode.Bounds.IntersectsWith(node.Bounds))
			overlaps.Add(node);
	}
	return overlaps;
} 

Code

private void OnNodeModified(object sender, NodeEventArgs e)
{
	RemoveOverlaps(e.Node, 20);
}

void RemoveOverlaps(DiagramNode modifiedNode, double minDist)
{
	var queue = new Queue<DiagramNode>();
	queue.Enqueue(modifiedNode);

	while (queue.Count > 0)
	{
		var node = queue.Dequeue();
		var nodeCenter = node.GetCenter();
		var overlaps = FindOverlaps(node, minDist);
		foreach (var overlap in overlaps)
		{
			var ovrCenter = overlap.GetCenter();
			var ovrBounds = overlap.Bounds;
			var dx = ovrCenter.X - nodeCenter.X;
			var dy = ovrCenter.Y - nodeCenter.Y;
			if (Math.Abs(dx) > Math.Abs(dy))
			{
				// offset horizontally
				if (dx < 0)
					ovrBounds.X = node.Bounds.Left - ovrBounds.Width - minDist;
				else
					ovrBounds.X = node.Bounds.Right + minDist;
			}
			else
			{
				// offset vertically
				if (dy < 0)
					ovrBounds.Y = node.Bounds.Top - ovrBounds.Height - minDist;
				else
					ovrBounds.Y = node.Bounds.Bottom + minDist;
			}

			// shifting the node might introduce new overlaps, continue processing
			overlap.Bounds = ovrBounds;
			queue.Enqueue(overlap);
		}
	}
}

List<DiagramNode> FindOverlaps(DiagramNode modifiedNode, double minDist)
{
	var bounds = modifiedNode.Bounds;
	bounds.Inflate(minDist - 1, minDist - 1);

	var overlaps = new List<DiagramNode>();
	foreach (var node in diagram.Nodes)
	{
		if (modifiedNode == node)
			continue;
		if (bounds.IntersectsWith(node.Bounds))
			overlaps.Add(node);
	}
	return overlaps;
}