"Namorada" and "noiva" (not "novia") are right, but "marida" isn't used as a word for "wife". Instead you use "esposa" or the expression "(possessive) mulher" where context dictates the possessive:
- "my wife" = "minha mulher",
- "your wife = "tua/sua mulher",
- "his/her wife" = "sua mulher", "a mulher dele/dela"
Yes, it can be said like that, but "Ele é meu homem" means "He is my boyfriend, husband, et cetera" in a funny way, as for girls who want to emphasise the boy the woman is talking about is with her. Whilst "(possessive) mulher" is very straight forward, it means "wife". If it is said to a woman who's not compromised, she could get offended, because it will most likely seem the man owns her, and that's rude.
Side Note: Although it looks like "minha mulher" means that I own this woman, it's not what's it's meant! But unfortunately yeah, it could be the initiative of using this term decades ago must have been because of a sexist ideal.
@Rick: Yes, if you say in Czech "moje žena" or in German "meine Frau", everyone will assume that she is your wife. You wouldn't say it if she were just your girlfriend. And the same with men. The difference is that in Romance languages it seems to only be used for women for some reason.