Static Resources and binding through XAML

you can get resources object from your code using FindResource method or Resources property of the FrameworkElement. Check if code below would work for you:

// find resource object
//string[] resource = (string[])FindResource("AllColors");
string[] resource = (string[])Resources["AllColors"];
if (resource != null)
{
    // old values
    foreach (var item in resource)
        Console.WriteLine(item);
    // set new values
    Resources["AllColors"] = new string[] { "red", "blue", "green"};
}
// find resource and show its new values
resource = (string[])Resources["AllColors"];
if (resource != null)
    foreach (var item in resource)
        Console.WriteLine(item);

though I don't think it's going to work the way you want it or it's a correct solution for your task. What you can do is define a class with colors collection:

public class TestColors
{
    public TestColors()
    {
        Colors = new ObservableCollection();
        Colors.Add("red");
        Colors.Add("blue");
        Colors.Add("green");
    }

    public ObservableCollection Colors { get; set; }
}

in your xaml you can define an ObjectDataProvider of the given object type and bind your control to its Colors property. Smth like this:

...
xmlns:local="clr-namespace:YourNamespace"
...
<Window.Resources>
     <ObjectDataProvider x:Key="AllColors0" ObjectType="{x:Type local:TestColors}"/>
Window.Resources>
...
<ListBox ... 
     DataContext="{StaticResource AllColors0}"
     ItemsSource="{Binding Colors}"/>
...

another way of how you can do it is binding your controls to a property of the window, smth like this:

public partial class MainWindow : Window
{
    public static string[] TestProperty
    {
        get
        {
            List result = new List();
            result.Add("red");
            result.Add("green");
            result.Add("blue");
            return result.ToArray();
        }
    }

    public MainWindow()
    {
        InitializeComponent();
     ...

xaml:

<ListBox ...
         ItemsSource="{x:Static local:MainWindow.TestProperty}"/>

update0: define resource in the code

// define resource in the code
Resources["AllColors1"] = new string[] { "red1", "blue1", "green1" };
// show new values
resource = (string[])Resources["AllColors1"];
if (resource != null)
    foreach (var item in resource)
        Console.WriteLine(item);

hope this helps, regards