This is because Gdi+ Image class is not thread safe. Hovewer you can avoid InvalidOperationException by using lock every time when you need to Image access, for example for painting or getting image size:
Image DummyImage;
// Paint
lock (DummyImage)
e.Graphics.DrawImage(DummyImage, 10, 10);
// Access Image properties
Size ImageSize;
lock (DummyImage)
ImageSize = DummyImage.Size;
BTW, invocation is not needed, if you will use the above pattern.