Hi,
By default DietPi will have RAMlog activated. Means /var/log will be a tmpfs and is located inside RAM. DietPi aims to reduce r/w operations down to a minimum.
ZRAM can be activated using /boot/dietpi/func/dietpi-set_swapfile zram
An overlayFS I tested once, some info on this link https://dietpi.com/forum/t/samba-fails-on-ro-filesystem/4123/2