The speaker explains that he has tried to replace this woman with other friends. The word "others" is used to indicate that these people are many and are not important. They are so insignificant that they do not need to be singled out. Also, the fact that he says that they "have been friends of mine" instead of saying that they still are his friends indicates that he either did not find them satisfactory compared to the woman he is speaking of, or that his other friends left him because he was not a good friend to them.
He goes on to say that despite his attempts to forget her, the woman is still on his mind. The images of death, sleep, and alcohol are all situations in which one does not have control of his thoughts. The speaker is showing that when he looks "death in the face" and he his so afraid that he cannot control himself, when he is sleeping and cannot control his subconscious, and when he is intoxicated, the woman's image comes to his mind. No matter how much he tries to suppress his feelings for her when he can, he cannot block her out completely. She is truly important to him, and that is why he finds himself thinking of her even if he does not want