Ethical Dilemma at University program
It sounds like you angry that the other students were "cheating" and got admitted to the PhD program while you were honest and were passed over. To add insult to injury, the professors seem not to care. Though you don't seem to have a clear goal in mind, I would suggest that it is to (a) achieve justice, and (b) not be handicapped in your final exams.

To the first goal, you should certainly report your experiences to the graduate director or another competent person. Even without proof, if they hear enough rumors, they will investigate, and things may be better in future years. 

Without proof, they are unlikely to do much. There is so much reasonable doubt. In particular, are you sure that the other students are  blindly copying solutions? At the graduate level, using solutions when you get stuck or to check your work may be appropriate (and student collaboration is encouraged)

Your claims about the exams are more worrying. Are you sure that the other students have exams? Are you sure that the professor knows this? 


If the professor might not know, it is fair to tell him. 
Without proof, the professor may not believe you (or may not care) -- as you say, he may just assume you are bitter and looking for someone to blame. 
You can provide proof by naming names. But you seem not to want to do this, and I don't blame you -- this could open a whole can of worms (i.e., questions about your integrity for not having voiced your concerns sooner).