Try to figure out what the strings that are being displayed badly have in common - as in what is their common source - they are coming from a different text files/databases/tables - that should give you some hints where is the source of the problem. PHP does not convert any text automatically so look at where it is originally located.
If you can pinpoint more exactly where the text start appearing garbled then we can help you better.
Some things you can investigate based on my personal experience with these types of problems:
First off ensure your .php document (the file itself) is of a correct encoding. You should be able to set it in your text editor or IDE. This can happen if you have copied over files from different places. If you have files not encoded in UTF-8 then convert them.
Secondly ensure that the data that you fetch into that file is being fetched using UTF-8 encoding. You may for example have some code that fetches data from a database where different tables have different encoding, or the text is being cast in different encoding, check this for more info: https://dev.mysql.com/doc/refman/5.7/en/cast-functions.html (let us know if you are using a different database like Postgres). You can try printing the string coming from a database right after it is returned - if it is fine but it is displayed badly on the page then obviously some bad formatting is being done afterwards and the database is fine.
Thirdly the text saved into your properly set up to utf-8 tables might get saved in a wrong encoding - you might need to correct it directly or check the code that does the saving into the database.
The database server also might be configured to serve results in a different encoding and you might need to set it up properly: Change MySQL default character set to UTF-8 in my.cnf?
Another option is for you to look for any functions that deal with conversion of encodings like http://php.net/manual/en/function.utf8-encode.php - it may be that something like that is happening unnecessarily and it is being done for a text that is already in utf-8, or is in a different encoding and you need another function.