Strangers in dreams can be very puzzling. Most often they are simply displaced persons and images that are drawn from the list of persons we know by face and name (sometimes they represent our own anima or animus). Strangers can reveal a tremendous amount of information about how we are experiencing the world. Different theorists have offered numerous explanations of who these characters are and how they worked into our psyches. Organizing the cast list is a useful endeavor for interpreting any dream.
Anima/Animus as Stranger
Carl Jung theorized that in the Self there were female counterparts to the male personality and male counterparts to the female personality. These counterparts are psychic projections that appear to us in dreams. When a female stranger shows up in a man's dream, her behavior can be a projection of the feminine side of his personality. This is conversely true for women who dream of male strangers. These strangers don't often have sex appeal for the dreamer, though some may. What is more common is a soul-mate friendship.
Understanding these characters is helpful because we learn how we want others (particularly the opposite sex) to perceive us. The corollary is how we are afraid they perceive us.
A second dimension to the anima/animus character is the desire to express what perhaps we are unable to express in waking life. Women may have animus characters in their dreams who show tremendous anger to compensate for a feeling that they cannot show in waking life. Likewise, men may have anima characters who cry due to the pain of life -- an emotion they may not feel the ability to indulge. These strangers are often benevolent to us. They may be helpful, protective, or supply information to solve a problem. When they are troubling, it is often because they are acting out in a way we wish we could.
This is when your dream moves a person from one type of relationship to another. An example would be having a well-known celebrity become your brother or sister. A more common example includes boss or teacher as a parent. In addition to personality roles, emotions might get displaced. This is especially true in the case of anger or sexual attraction that cannot be expressed in waking.
These are stranger-lovers who appear in dreams to have sex with the dreamer (an incubus visits a female; a succubus visits a male). They often represent the extremes of the sexuality experience. Either they are idealized lovers in the emotional and physical sense, or they are demonic and repulsive lovers, employed to steer you away from a waking practice that you may know is bad for you.
These are strangers of the same gender as the dreamer who possess the negative attributes of the dreamer. Most often, these negatives are presented in extremes. It is a very useful situation for understanding ourselves. Each of us has negative traits which we try to cover-up in our public life. Sometimes, we may even develop denial defenses in our egos to refute that we have downsides to our personality. These shadow strangers appear in our dreams to show us our weaknesses.