You may serch for the usages of the words ( at www.baidu.com, for instance） so that you may find out the subtle semantic color and the exact contextual speciality.

Briefly speaking, 开心 and 高兴 refer to the instant feeling or mood of a person, and they are more casual than 快乐 and 幸福. 开心 was once mainly used by the southern people and 高兴 is northern and today they keep some regional tone still, but today both are used in the north and the south. 快乐 and 幸福 are more formal. 快乐 mainly means the mental state of a person, and 幸福 the condition of living.