Oxygen disables theme so how do I manage functions.php?

First thing you notice when you install Oxygen is that is disables the theme.

So you can't anymore use your functions.php to add whatever you were used to add when using themes.

But you can achieve the same thing by using Code Snippets plugin (free) or Advanced Scripts (paid but worth it: $39.99 for unlimited websites, lifetime updates and support - link is affiliate link but that's not the reason why we recommend it, see James' advice or Mohammed's).