The answer is: Not much, really.
Except for this- there is something that happens in all three situations that can have therapeutic benefits. No, I'm not suggesting you tuck a flask into your Sunday best, nor do I recommend showing up to yoga class drunk (I've taught an inebriated person once- it wasn't fun for him). All three situations involve group singing on some level, which has been shown to "produce satisfying and therapeutic benefits, even if the sounds are of mediocre quality". (AKA even if you make your dog howl when you sing in the shower, belting it out in a group setting can still feel good for you.)
While singing doesn't occur too often in most yoga classes (unless you're in Will Blunderfield's class- that man has the voice of an angel); chanting, or even saying the word "om" to start and end a class is pretty common. What's the deal with OM? You will often hear yoga teachers say that "Om" is the sound of the universe. It connects us to all things. And really, it isn't too far-out-there to say so. As explained by my dear skeptical scientist friend: The "mmmm" part of "Om" mimics the sound of a vibration- and essentially all particles, all atoms, vibrate on some level. In addition to all that, "Om" is also a good way to create a mini community for the hour. It synchronizes the group. Have you ever noticed how your "Om" may be a different pitch on different days, depending on your teacher or the other yogis around you? We take in auditory cues and adjust accordingly. The same goes for singing in church. This attempt at coordination forces us to think about what someone else is doing and pulls us out of ourselves/ out of our own heads. As this podcast mentions, it activates the frontal cortex of our brain which is the part responsible for how we see ourselves in the world- whether we are alone, or accepted in a group. You're not just doing your own thing, all on your lonesome. Instead, you start to see the part you play in the whole. As if all this wasn't good enough, singing together also releases oxytocin which increases social bonding and trusting relationships.
You might be wondering- cool story bro, but where do drinking songs come in? Well, since we're often way too wrapped up in our own heads to belt out songs with people around us, (you know, that little voice that tells us we aren't good enough) the only time most of us get in any group singing is when we're four drinks in and have left our inhibitions on the floor of the bar.
So what can we make out of all this? Two things:
1.) Maybe give "Om" a chance. If you've been holding back in your yoga class, I dare you to OMM from the rooftops at your next class and see how you feel.
2.) Feeling down? Take a yoga class, go to church, or grab some friends for a group karaoke night.