The house's room - ev(in) ev + genitive (ın) and then room possessed (not by ghosts but by house) oda(s for vowel + I possessed) odası. You have to take into account vowel harmony. Bir gives us a room, hence 'a room of the house' . I think that's all correct. Someone will correct me if I'm wrong hopefully
Esma, "evin" is "ev+in"="the house". "In" is the genitive suffix, third person singular, because "the house" is the possessor of the room. You are rigth when you write "your house"="evinin bir odası", "ev+in+in" : the first "in" for "your" and the second one, the mark of possession "of".