Very interesting post. Here's my take.
1) Vertigo - Elevation
I'd say that lyrically, neither song is terribly strong. But I get the sense that Elevation and Vertigo could both be describing the same scene, just at different time periods. For example, Elevation could be the beginning of a party, when everything is still going well and everything feels good... and Vertigo could be the party at the end of the night, where the drinks have started to kick in and the place is getting a little bit seedy. Maybe I just have a wacky imagination.
Alternatively, one could pair Vertigo with 11 O'Clock Tick Tock. I guess maybe those two songs are thematically similar, and as you'll see from what follows, I pair more songs with ATYCLB than anything else. Trying to avoid that.
2) Miracle Drug - When I Look at the World
If you know what Miracle Drug is about, this pairing makes more sense than it would otherwise. See
http://hem.bredband.net/steverud/U2MoL/HTDAAB/md.html for a transcript of Bono's explanation of MD from the free Brooklyn Bridge concert. WILATW refers more directly to what God is seeing, and how he reacts... but I think a connection could be argued for the paralyzed boy as well.
3) Sometimes You Can't Make it on your Own - Kite
I think this connection is pretty clear. Moving on...
4) Love and Peace or Else - Like a Song
Both show clear anti-war seniments, both have a hard and driving force in the music, both call for hearts to be cleansed; to start anew. Like a Song is more straightforward, I suppose, but both songs share the same goal.
5) City of Blinding Lights - Where the Streets Have No Name
Probably an obvious connection; the song is written specifically with the Elevation New York City show on 10/24/01 in mind; even more specifically, how the crowd looked when the floodlights were turned on during WTSHNN. I was there that night. Unreal.
6) All Because of You - Gloria
I haven't quite figured out yet if I think this song is about Bono's mother, or God, or whoever else. If one contends that ABOY is about God, than Gloria pairs up nicely with it. Both songs praise the entity in question. "Only in you I'm complete." And so on.
7) A Man and a Woman - All I Want is You
Ugh, I got nothin' for this one. It doesn't help that I don't like AMAAW, either. *shrug*
Crumbs from Your Table - One
As much as I'd like to pair CFYT with Walk On (because CFYT is ruined for me due to how similar the chorus is to parts of Walk On), I'll go with One. I mean, if you're introducing U2 to people, you damn well better include One. And both songs tell a type of "we get to carry each other" story.
9) One Step Closer - The First Time
Besides being similar sonically, One Step Closer could be looked at as kind of a "Part 2" to The First Time. Here's my girlfriend's take: "TFT is about the Prodigal Son willfully leaving his father's house and all the love and riches therein. OSC is that Son returning after many years to find... what? The house fallen down? His father dead? Or dying, maybe. In any case, the Son is older and sadder, and things aren't as he left them.
10) Original of the Species - Shadows and Tall Trees
I see OOTS as talking to a teenager. I see SATT as an angsty teenager talking. "Do you feel in me / Anything redeeming / Any worthwhile feeling / Is love like a tightrope / Hanging from the ceiling?" Whine, whine, whine! ;-) Alternatively, you could probably match OOTS with some other songs off of Boy.
11) Yahweh - Wake Up Dead Man
"Yahweh, tell me now / Why the dark before the dawn", etc. Two songs that ask God "what's going on?" Both songs have the singer waiting for the proverbial dawn. WUDM is just more insistant.
As for songs that are necessities in any introduction to U2... if I had to shave the list to ten songs:
One
WTSHNN
Mysterious Ways
Walk On
Sunday Bloody Sunday
Pride
ISHFWILF
I Will Follow
Bad
Please
Video clips and live performances... I could write a book. =P