What positive effects does sports massage have on tennis elbow?

Less Pain: Sports massage and other types of manual therapy can increase range of motion of joints and blood flow to tissues, for example the tissues affected by the inflammation associated with tennis or golf elbow.

Tennis elbow: Not sure what you mean by sports massage, but one effective method to lessen pain associated with tennis elbow is cross frictional massage. May be done using finger tip or cube of ice. Rub with increasing amounted pressure perpendicular to the direction of the fibers of the extensor muscles of the forearm. Couple with stretching exercises can be quite helpful at reducing symptoms.