Which one is gramatically correct in this case and why?

[RobertC]

- Missionary school of English and Portuguese
- Missionary English and Portuguese School
- English and Portuguese Missionary School
- The Missionary school of English and Portuguese
^
Thanks in advance. :D

[Firefox]

I'd like to help but not sure what this school IS.

Is it a school of mixed English and Portuguese nationality or ownership?
Is it a school that teaches the English and Portuguese languages?

Assuming that the school does in fact teach the two languages, I believe your first and last examples are correct:

- Missionary School of English and Portuguese
- The Missionary School of English and Portuguese

[elmirau]

I think last one probably more likely to be correct

[Joe]

The last one is more formal but both are possible.