How can I check multiple textboxes if null or empty without a unique test for each?

Sure -- enumerate through your controls looking for text boxes:

foreach (Control c in this.Controls)
{
    if (c is TextBox)
    {
        TextBox textBox = c as TextBox;
        if (textBox.Text == string.Empty)
        {
            // Text box is empty.
            // You COULD store information about this textbox is it's tag.
        }
    }
}

Building on George's answer, but making use of some handy LINQ methods:

if(this.Controls.OfType<TextBox>().Any(t => string.IsNullOrEmpty(t.Text)))  
{
//Your textbox is empty
}