What are Sartre's definitions of these three term "anguish," "forlornness," and "despair"? How does he distinguish among them?

The terms identified helps to articulate how Sartre views human consciousness.  The sense of "forlornness" results from the rejection of all transcendental and totalizing ideas. When Sartre argues that human beings are "forlorn," he is stressing the idea that they are without any sort of guidance from transcendent ends.  They are trapped with only their sense of freedom present, which brings about a natural condition of "anguish," in that nothing nor anyone can help to alleviate the pain of isolation and loneliness, the condition of individual freedom, and more importantly, having to choose.  It is this choice that causes "despair" for nothing can lighten the burden of the agony of choice.  Take, for example, the student to whom Sartre alludes.  Loyal to his country, the student enlists in the French Resistance to the Nazis, but ever loyal to his mother, he realizes that if he leaves to fight for nation, his mother will die alone of a broken heart.  The student is poised between equally desirable, but ultimately incompatible courses of action, and represents the essence of human consciousness.  He is forlorn, for both loyalty to nation and to mother helps to cancel one another out.  One cannot overwhelm the other, making totality a moot point.  Additionally, the student is forlorn for nothing can decide for him, only he can, and because of this, anguish and agony results.  Freedom becomes brutal, as human beings become actors who are thrust onto a stage to perform without scripts or the aid of a director.  Only the glare of a spotlight and the obscure faces in the dark remain.