I've been using PHP for roughly 10 years now. I can't count how many times I've run across "functions.php" or "library.inc.php" or one of its many equivalents.
It's a bad idea. Don't do it. If you find yourselfs writing files like that, stop it. NOW.
It's not a matter of OOP vs functional programming. It's a matter of organising your code. Group your functions and variables properly and OOP will feel natural. If your functions do many things and don't lend themselves easily to being grouped, try to refactor them so they only do ONE thing at a time. You'll find that this also lets you strip a lot of redudancy out of your existing functions.
You can use OOP to encapsulate your code further: put your variables into objects and have the functions that operate on these variables either be property methods of those objects or interact with these objects as input. Avoid "global" and don't modify your function arguments routinely.
Your problems aren't the problems you think you have.
EDIT: As for your example: since strings aren't objects in PHP, you can't really put that function in a sensible class, so you'd probably want to put it into a utility module with other string functions and use it as you already do. Still, tearing apart your functions.php and turning it into a collection of atomic modules does wonders to your code's readability. You may find a file containing assorted functions readable because you are familiar with its contents, but another coder (and "you after three months of not using the code" IS another coder) will not.
EDIT2: Please understand that "OOP" doesn't magically make everything better. It's a tool that is supposed to help you writing better code. If you use OOP everywhere, you're probably doing it wrong (or writing for Java *cough*
). If you use OOP without understanding things like structured code first, you won't get anything out of it, either.