Move window without border

This Code Project article should help you accomplish this. I've used this myself with no problems. This is the jist of it:

public const int WM_NCLBUTTONDOWN = 0xA1;
public const int HT_CAPTION = 0x2;

[DllImportAttribute("user32.dll")]
public static extern int SendMessage(IntPtr hWnd, int Msg, int wParam, int lParam);
[DllImportAttribute("user32.dll")]
public static extern bool ReleaseCapture();

private void Form1_MouseDown(object sender, System.Windows.Forms.MouseEventArgs e)
{     
    if (e.Button == MouseButtons.Left)
    {
        ReleaseCapture();
        SendMessage(Handle, WM_NCLBUTTONDOWN, HT_CAPTION, 0);
    }
}

This will basically "trick" the window manager into thinking that it is grabbing the title bar of the winform.

To apply it to your project, just use the MouseDown event from the MenuStrip.

Here is the .Net Way

    private bool dragging = false;
    private Point dragCursorPoint;
    private Point dragFormPoint;

    private void Form1_MouseDown(object sender, MouseEventArgs e)
    {
        dragging = true;
        dragCursorPoint = Cursor.Position;
        dragFormPoint = this.Location;
    }

    private void Form1_MouseMove(object sender, MouseEventArgs e)
    {
        if (dragging)
        {
            Point dif = Point.Subtract(Cursor.Position, new Size(dragCursorPoint));
            this.Location = Point.Add(dragFormPoint, new Size(dif));
        }
    }

    private void Form1_MouseUp(object sender, MouseEventArgs e)
    {
        dragging = false;
    }

that's it.