I have an Android phone running ICS, and a while back I got an app from Google called Listen, which I could use to, well, listen to podcasts I’d subscribed to through Google Reader. In August, Google stopped supporting Listen and disabled the search function on the app, but I could still use it to listen to my Reader-subscribed podcasts.
So in the next ten weeks I’m looking for an app that will let me subscribe to podcasts and sort individual downloaded episodes in an arbitrary order, and is free. If nothing like that exists, I’ll give up free, but the feature of Listen that I really liked was being able to queue a bunch of podcast episodes and make a playlist; the two I’m trying now don’t let my reorder downloaded episodes.
That’s the one I use as well. I don’t have much to compare it to, but it was highly recommend.
Just go to the Play Store and search for “podcast” or “podcatcher” or “podcast receiver”. They should all bring up results and then take a look at the reviews and pick one. If you pick free ones, you can try a few out and find the one you like most.
Also, I would suggest you set it to only update when it’s plugged in. Whether that’s an actual setting or you tell it to update at, say, 2am, when you would have it charging. First of all, you’ll likely kill your battery and second, I had one phone that would get so hot while it was downloading new podcasts, I’d have to take it out of my pocket.
I use BeyondPod, as it has a ton of features. There is demo period where you can try the full version, but once that expires, you lose some features as it reverts to the free version.
I’d say it’s worth a try, as it offers the functionality you’re looking for, though I’ve seen more intuitive programs.