I've never found a mobile podcast app that I like. Something about having an extra app to manage audio files didn't appeal to me. In recent years I landed on Poweramp as my Android media player of choice as it allows me to use directories on my filesystem directly.
I've accumulated a few podcasts that I listen to regularly and I've used IFTTT to email me when an episode releases and then downloaded them manually to my phone's SD card. I started listening to The Green Box Podcast which infuriatingly didn't name their mp3s nicely so I ended up hacking together a piece of Python and scheduled it on a cron job to check weekly which downloads, names and tags each episode neatly. I just discovered the MalwareTech podcast so I decided I'd write another script to handle that one. In doing so I figured "why not make this generic" and lo podcast.py was born.
podcast.py takes a --list parameter which refers to a text file containing podcast subscriptions.
The podcast list needs to be formatted as $podcast_feed_url $name_to_use_as_artist_and_album $output_directory.
The final piece of the puzzle for me is notifying me when something new is downloaded, at the moment my thought is to output an amalgamated RSS feed to my web server which my RSS reader can pick up and display.
Like I said, it's janky and weird. You should see my plans for replacing invidio.us in my RSS feed. I'll probably write about it once I get something working.