Is a landlord allowed to put a "random" roommate in an apartment with other people?
(My 2 roommates and I signed a lease for a 4 bedroom apartment, and the landlord filled the fourth room with someone we did not know and they did not tell us until we moved in)

Let me see if I have this right. You and your roommates signed a lease for a 4 bedroom apartment and all of a sudden the 4th bedroom is rented out by the LL? If I were you, I would definitely pull out the lease and look it over. Is this mystery roommate paying rent to the roommates or to the landlord? It sounds like to me he is leasing the aparment out by the bedroom. Another words, you pay a certain amount for your room, roommate 1 pays for his room and etc. Whose name are the utilities and such in?

I would have a problem having a complete stranger living with me.

Well, we all pay the landlord and it is rented out by the room. Also, utilities are included in the rent, so they aren't in anyones name.
And, it is causing so many problems having her live with us. She runs up our power bill so we go over our allotement every month, she refuses to compromise on anything, and any time we try to talk to her about anything, she gets the biggest attitude and accusses all of us of racism, etc.