Pocket Casts is probably the best podcast app available for Android; it’s certainly a favourite here in the Clove offices. It isn’t free but it’s definitely an app that’s worth paying for on Android.
The good news is that it’s about to get a lot better – it’ll soon have a desktop app. The desktop interface is currently under closed beta so you probably won’t have access yet, but here’s the link in case you want to give it a try.
Download Pocket Casts here from the Play Store