Here's my analysis of the album. Apologize in advance for any formatting errors.
American Idiot
Our story begins with Jesus hearing something on TV or on the radio about something that happened during the Bush administration. Possibly war. He goes full Jimmy and goes off on a rant about Bush and all the problems with him and just America in general. He talks to himself with his Jesus and Jimmy personalities clashing and fighting with each other, as Jimmy has much more uncaring and not give a fuck type views than Jesus.
Jesus of Suburbia
This song has multiple parts so I'll split it up a bit. I like to think this whole song encapsulates the kind of mental breakdown that Jesus goes through that leads to him running away.
I. Jesus of Suburbia
This is Jesus after his little meltdown, walking through town and reflecting on who he is as a person and what's wrong with him. It's about him just reflecting on all of his issues, and just everything wrong in general.
II. City of the Damned
This is about the problems with his country and Jesus reflecting on them and realizing how fucked up his country is and all the problems that Bush has brought onto the country. Some of the lyrics reference things like war and poverty. I like to think this song is him arriving to the 7/11 and you'll see why I think that in the next song.
III. I Don't Care
This is our first real glimpse of Jimmy. This song is about the personality of Jimmy coming out and talking about how he doesn't care anymore. Time and time again he's seen that everyone's full of shit, born and raised by hypocrites, that nothing will ever change that he should really just stop caring. I like to think he's at really just stop caring. I like to think he's at the 7/11 that he mentions so much in the song just wrecking the place like he does In the music video. Then he runs off and that leads into the next song.
lV. Dearly Beloved
This is from Jesus again, and talks about all the therapy and shit he's had to go through and how it's all stupid. How he's him and that's all he's ever going to be and that's it. This whole song is kind of mocking the therapy that he's been taking and just talking about how full of shit it is.
V. Tales From Another Broken Home
This song is about Jesus getting home. His mother tells him the police have been there and asks where he's been and they get in a fight. At the end of the fight he goes full Jimmy, screaming and running away from home. He gets in his car and drives off
Holiday
This is St Jimmy mostly, and revolves around the excitement and recklessness of his road trip, which is why it's so upbeat. He's taking a "Holiday" from life and that's in part what this song is about. Taking a holiday from life, worries and the world in general. It's also very political, as Jimmy is making fun of the world today and everything that's wrong with it instead of taking it in a more serious way like Jesus. This is why there's that "Sieg Heil to the president gas man" thing, which could quite possibly be triggered by Jimmy listening to the news through the car radio.
Boulevard of Broken Dreams
The car breaks down on the highway and the sudden realization of what Jimmy did hits him and he turns back to Jesus. He walks aimlessly looking for anything and realizes that he's all alone out here now. Clean slate. No family. No friends. Nothing at all.
Are We The Waiting
Jesus of suburbia finally comes across a city, and it's huge! Way bigger and better than the shitty small town with the 7/11 AKA Jingletown! This song is Jesus wandering through the city with wonder (Skyscrapers, stargazers in my head) and coming across a local tavern. He goes in and hears everyone chanting and singing an inspiring song with their buddies and he joins in singing it. Are we we are, are we we are the waiting. They scream it from the top of their lungs and so does Jesus.
St. Jimmy
The sudden excitement of the new city hits Jesus like a transport truck and out comes Jimmy. He has a night of havoc in the city. Drinking, partying, sex, drugs you name it. I'd like to think he's at maybe a local Casino? Gambling his money away but having the time of his life.
Give Me Novacaine
This is Jesus of Suburbia waking up the next morning in a seedy motel with a shitty hangover and no one there for him. The loneliness hits him once again. He wishes for someone to be there for him to comfort him and help him through (Give me a long kiss goodnight and everything will be alright) he gets up and happens to glance through the window when he suddenly sees her. The girl of his dreams. He sees her through a window across the street and just by looking at her he knows that she's everything he's ever wanted and more. This is why she's a rebel transitions into this song out of nowhere.
She's A Rebel
This is Jimmy's point of view on the girl. He thinks of all the rebellious things they could do together. He gets excited that he'll finally have someone to do all these reckless things with. A partner in crime, so to speak. And her name is Whatsername.
Extraordinary Girl
This song is Jesus admiring Whatsername and all of the amazing things about her. I'd like to think Jesus and Whatsername are living together at this point and it's been maybe a year? And how Jesus still loves absolute everything about her. He reflects on the ways they've made each other's lives better and the things that have gone on. He also reflects on all the fights they've had and shit they've been through and thinks to himself how crazy it is that even after all that he still considers her an extraordinary girl.
Letterbomb
Jimmy, on the other hand, is getting sick of Whatsername. He wants a new girl as he is a womanizer type of guy. They get in a big fight over this and Whatsername leaves and vows to never come back, just like Jesus did at the beginning of our story. (She said I can't take this place I'm leaving you behind, well she said I can't take this town I'm leaving you tonight). She says it in a letter, and this is why the name of the song is Letterbomb. As someone else said, he receives the letter, and it hits him like a bomb.
Wake Me Up When September Ends
This song is about Jesus of Suburbia realizing what he's lost with losing Whatsername. Yes I know it's about Billie's dad but just forget about that. In the context of the album, this song is mourning the loss of his perfect dream girl Whatsername . The harder Rock sounds in this song I like to think are Jimmy trying to break through and tell Jesus that he doesn't care, but Jesus represses those feelings and doesn't let them take him over.
Homecoming
This song is once again split into parts so I'll do the same thing I did with JoS.
I. Death of St. Jimmy
This is Jesus realizing how Jimmy has always been more harm than good to him and ruined the best thing in his life for him, so he goes to the docks, sits by the water, and gets rid of Jimmy for good. He decides it's time to man up and grow up. Which leads to...
II. East 12th Street
We learn that he got a job at a facility in the city. That he's growing up and working at a serious place. But he still reminisces and wishes he was back in his little town hanging out with the underbelly as this job just doesn't feel like him. As a result of all of this uncertainty he goes on a drinking binge which leads to...
lll. Nobody likes you
He gets depressed after thinking of Whatsername . I like to think this song is the leftover voice of Jimmy in his head berating him over who's he's become. He's gone from an Anti-establishment punk to a working for the establishment opposite of punk, and Jimmy makes it clear what his feelings are for Jesus.
lV. Rock n' Roll Girlfriend
This song is basically his vision of Whatsername's boyfriend bragging about having her and all the good stuff about her. He thinks of how their lives must all be so much better than his and how off track he is with his life. How he's become the opposite of what he's always wanted to be. Which leads us to...
V. We're Coming Home Again
This is Jesus quitting his job, leaving the city and going back home. He talks of the people he sees and the places he used to hang out at (7/11 being referenced again) he finally decides to forget about his life in the city and just go back to this town that, even though he hated it before, is his favourite thing in the world. ("So send my love a letterbomb" references that he doesn't care about Whatsername anymore and that he's trying to forget about her along with his old life)
Whatsername
This song is about him, many years later, maybe reminded by digging up an old picture, and reminiscing about his time with Whatsername and in the city, and reliving it one last time, so that he can relive it one last time, so that he can finally completely move on from that part in his life (he references burning all of the photographs), and live without the pain of that breakup in his heart forever.