

I used to use Airsonic. Suporte auto downloads of podcast episodes.
It worked for me as I mostly listens to music and 1 or 2 podcasts once and a while. Not listened to podcast for a while so might use just Antenna Pod.
I have also moved on from Airsonic to LMS (Lightweight Music Server) and use Ultrasonic on mobile.
LMS is also pretty damn light as well. Uses about 19 MB of RAM on my system on idle.
Lightweight Music Server