I have an LG android phone and I listen using the youtube app right on my phone. If you don't have the app my daughter listens to some of her podcasts (too many if you ask me as I have a total of 12 subscriptions and she has over 30) on my phone using the web browser and just typing in youtube.com when we are out and about (her ipad is internet only).
If you want to listen to just audio you can use the dis unplugged app in the google play store. I will warn you if you have to turn it off part way through it is not easy to do. I usually end up powering off my phone and I have not figured out how to pause a playing. Unless I know I can listen uninterrupted to an entire podcast I tend not to use this one.
I am able to watch live though the youtube app haven't tried with the other 2 ways I have mentioned.