Smallest circuit to make a sound
Perhaps the least-effort option that meets the specified requirements is to use a piezoelectric buzzer, such as this one:



They can be had for under US$1 from various sites like eBay.com.

This datasheet lists a number of such buzzers: Stay away from the ones that specify "without circuit" or "external drive type".

A MOSFET or BJT as a switch, driven from the microcontroller GPIO pin, is sufficient to operate the buzzer. 

These buzzers come at a wide range of "annoying" sounds, pick one to your liking.