In your DataGridTemplateColumn you have SortMemberPath set to “”. If you set this to an actual property on the item (say, CompleteDate), you should be able to sort. You can also set CanUserSort=”true” or CanUserSort=”false” on selected columns.

SortMemberPath gives the property to sort on when the user attempts a sort. If this isn’t set, then the grid doesn’t know how to sort that column ( it does not use the text in the column)
Ex:

<ListBox x:Name=”lstbxTest” Width=”100″ Height=”100″ Margin=”239,407,301,0″ VerticalAlignment=”Top” ItemsSource=”{Binding}” d:LayoutOverrides=”Height”>
<ListBox.ItemTemplate>
<DataTemplate>
<StackPanel Orientation=”Vertical”>
<TextBox Text=”{Binding EmpId}” VerticalAlignment=”Top” HorizontalAlignment=”Left”/>

</StackPanel>
</DataTemplate>
</ListBox.ItemTemplate>

</ListBox>
<data:DataGrid x:Name=”DGTest” Height=”89″ HorizontalAlignment=”Left” Margin=”137,342,0,0″ VerticalAlignment=”Top” Width=”90″/>

CS File:
this.DataContext = EList;
DGTest.ItemsSource = EList;
btnTest.Click += new RoutedEventHandler(btn_Click);

http://codebetter.com/blogs/karlseguin/archive/2008/11/27/back-to-basics-delegates-anonymous-methods-and-lambda-expressions.aspx