I've run into this issue as well and for me it was solved by playing music in the Music app and turning the volume up there, then switching to Overcast and turning the volume up in it (using the crown). I'm not sure if this solution works for everyone or if the issue some people are experiencing is a separate one, but it worked for me.
It seems like the Music app (and potentially Now Playing?) adjusts a global/system volume level, while all other apps have their own internal volume level that acts as a percentage of the system level. i.e. if the system volume level is at 50% and Overcast's level is 75%, the output volume would be 37.5% (75% of the system's 50% level). But this is just my experience/theory... who knows what the true behaviour is.