Hello,
I wonder if the output voltage on the i/o pins equal the VCC used to power the MCU, or if there is a notable difference even under very low current drawn from the pin. To be specific I need 3.3V out and I wonder if it is suitable that I run the Atmega (328-PU) with 3.3V, or perhaps 3.4V?
Typical XY problem! 
This will depend on the current in the output.
Below is an extract of the datasheet of 328p. Same graph exists for Vcc = 3.3V.
Always read the datasheet
Thank you for providing the graphs. I took a look in the complete datasheet but I simply didn't manage to find them!
This may be an impossible to answer follow-up question, but what kind of load could I assume from an ILI9341 or ST7735 display? Anyone with any experience of them? The problem is that I have limited volume and cannot find space for a voltage divider or logic level convertor, so I aim to interface with the display directly from the digital outputs of the Atmega328-PU.
Paul__B:
Typical XY problem!
Almost as annoying as snarky responses made knowingly that it won't contribute anything at all to the question asked.
The xy problem link is a very very good read.
Load on data pins is negligible under normal conditions, they're seeing the full output voltage (well, if it's a higher voltage than the device can tolerate, there will be a load through the protection diodes, at least until it fails)
To interface with something that uses different logic voltages, use a level shifter.
teapottaxi:
Almost as annoying as snarky responses made knowingly that it won't contribute anything at all to the question asked.
It is not obvious what you meant there, but indeed you have addressed the XY problem by now revealing what you really meant to ask after all, and should have asked in the first place. 
Whilst I cannot imagine why you would ever want to connect an ILI9341 to an ATmega328, its input characteristics (page 236 of the manual) are standard 3.3 V CMOS specifications for which the ATmega328 is designed.
