Do not create your own SolidColorBrush instances, but use the predefined ones from the Brushes class:
Ellipse obj = new Ellipse()
{
Name = "",
Width = width,
Height = height,
Fill = Brushes.Transparent,
Stroke = Brushes.Red,
};
...
if (obj.Stroke == Brushes.Red)
{
obj.Stroke = Brushes.Green;
}
else if (obj.Stroke == Brushes.Green)
{
obj.Stroke = Brushes.Red;
}
else
{
obj.Stroke = Brushes.Gray;
}