I need some help translating the months of the year into the header. They are being shown in English (APR, for example).

Please share the screenshot of it where it is displaying.

Also please share all the strings which are not getting translated for you.

How can I do to display in Portuguese? (My WordPress is set to the correct language).

You are translating your site so you may be translating it in to Portuguese so i am not sure what do you mean by this?