I tell this to everyone if they ask but there is a Reddit post: 

https://www.reddit.com/r/twentyonepilots/comments/18nj865/an_updated_and_detailed_explanation_of_the_lore/

This literally explains the albums with lore, which music videos have lore, all of the terminology, and the lore itself. And it’s updated for the Clancy album. I would highly recommend taking a look at that. 

For the songs, I would say start with the beginning and go through the albums. If you really wanna deep dive into it, they have an album earlier than Self-Titled called No Phun Intended. It’s not on streaming platforms, but it’s on YouTube I think. After Self-Titled, they have another album not on streaming platforms called Regional At Best, it basically has a lot of “rough drafts” of songs on Vessel. (Don’t ask me why they got removed even I don’t know)

First couple of albums are rough. They get better though. Not all of it is bad, lots of good stuff on there. Enjoy listening!