Filtering out OLED electrical noise
A large (330uF) capacitor between VDD,VSS is definitly worth doing but you should also investigate tweaking your OLED init code.  Many OLED's have lots of config options to do with voltages and frequencies that can really make a difference to the amount of electrical noise they make by reducing their overall current draw but also by altering the "pattern" of said current draw.

I had the same problem as you with SSD1327 OLED from waveshare. The default configs work great but produced a significant amount of noise in my audio output.  The main turned out to be the refresh rate that was well into the audible range at around 120Hz and much higher than actually necessary.  A bit of tweaking to the internal oscillator config reduced the frame rate to a much lower value leading to less noise in the audible range. Futher tweaking to drive voltages reduced the scale of that noise so much that is almost unnoticable in my application.

I wrote more about it over on the EEVblog