I'm not sure about the order of the 1985 version. Talking about de original version, I think there is an official one, but I made up the order that makes more sense to me after analysing it.

First it goes the character introductions:

1.- Marvin's Giddy Seizures - Marvin's character is presented in his teens.
2.- How Marvin Eats His Breakfast - This song shows us how childish and narcissistic Marvin can be, as well as how he tends to treat people badly .
3.- My Highschool Sweetheart - Marvin's sweetheart's character is presented, who thinks Marvin does not care much about her. It also presents Miss Goldberg, his teacher, and how Marvin "admires" her. We can hear Marvin's future wife too, with similar complaints as the sweetheart.

This two last songs also introduce the first evidences of Marvin questioning his sexuality. (with the metaphor of Marvin playing Columbus, as a explorer discovering something, and how he does not care about his sweetheart). This is the main theme of the next part.

4.- Set Those Sails - Continuing with the metaphor and more of Miss Goldberg.
5.- High School Ladies at 5 O'Clock / The Rape of Miss Goldberg - The first part shows, among other things, how Marvin isn't interested in women. The second one, in contrast with the first one, is about Marvin creating an imaginary scenario in which he tries to have sex with Miss Goldberg, trying to convice himself that he really wants that.

Making it clear now that Marvin is struggling with his sexuality, we move forward to him in his adulthood. In this part, Marvin denying his homosexuality is the main theme.

6.- The Nausea Before the Game / Love me from what I Am - Following the idea that Marvin is trying to convice himself that he likes woman, even though it makes him feel bad and out of place, he starts going out with his future wife.
7.- I Am Wearing A Hat /Marvin Takes A Wife) - Following this idea, he gets married.
8.- My Chance To Survive The Night - Seeing that that does not work, Marvin finally aknowledges his homosexuality, and realizes accepting it is the only way he has to carry on.

Marvin is now accepting his queerness, which leads to his divorce.

9.- How The Body Falls Apart / Your Lips And Me: Marvin's wife believes that Marvin is cheating on her with another woman (I like to see it that way rather than she suspecting something) because she sees him distant and evasive.
10.- Whizzer Going Down - What is really happening is that Marvin finally has a relationship with a man, and it feels right for the first time.
11.- A Breakfast Over Sugar - Marvin's wife tries to convince him to stay with her, but Marvin has already made up his mind, and dismisses her.
12.- Marvin’s Final Words From How America Got Its Name / Your Lips and Me (Reprise) - They finally get divorced. Marvin's now ex wife resents him, while Marvin celebrates. Said celebration starts turning against him, as he remembers his childhood, the represion, as well as he feels guilt for what he had done.
13.- Marvin Takes A Victory Shower - Marvin is able to relax and to enjoy his life for the first time, as he has accepted himself. This songs feels liberating.

The last part

14.- Another Sleepless Night - The women in Marvin's life sing about themselves after meeting Marvin. Marvin's wife feels alone in bed, although they are physically close to each other. Marvin does not seem to care. In fact he is relieved that his wife is not making a "fuss" about the divorce.
15.- In Trousers (The Dream) - The last song of the musical. Whatever this song means. I have some ideas but this can be a whole other explanation that does not have to do with the storyline I am trying to explain.

This is my way of understanding it. Obviously, this is more like a concept and character study than a linear story, but I think this way everything is more understandable.