SLEEP_MODE_ADC interfering with USART (and beep)
Is it expected that USART tx/rx gets disturbed by SLEEP_MODE_ADC?
  


Absolutely. Both the USART and timers use clkIO for operation, and this is disabled in ADC Noise Reduction mode.


  
  Does sleep mode actually make sense in combination with oversampling? Does some noise maybe not even help to increase accuracy (dithering) or does that apply only to noise coming from the sensors?
  


You actually do want some noise when performing oversampling and decimation as you are, so I don't feel that ANR mode would make sense here; restrict your self to Idle mode (SLEEP_MODE_IDLE) in order to keep the USART and timers alive.