Translation sites are generally poor, especially with Latin. As far as these words go, it's a good idea to look at a Latin-English/English/Latin dictionary
Service: Depends on the sense of the English word. It could be something like servitium (i.e., servitude or slavery), or officium or ministerium (i.e., public service). Or moenus ("a favor," "a solid.")
Slave is servus, servi for male, and serva, servae, ae or ancilla, ancillae (handmaiden) for female.
Savior is "salvator." Just like El Salvador, or to resort to some Church Latin: "Salvator mundi, salva nos, qui per crucem et resurrectionem tuam liberasti nos."