As I said before, I didn't participate either, but I have a pretty good understanding of it since basically everything is hyping the stream.
All the Pokemon that were caught during the Red playthrough are listed here on Bulbapedia, including the countless Pokemon released during the experiment. I've tried to gather an explanation of all these nicknames and "stories" each Pokemon were given, so here it is...
Pokemon that won in the Pokemon League
- AA-j the Zapdos, who was well known by fans for how long it took to get it into the party. A bunch of Pokemon were accidentally released in the process.
- AAAAAAAAAA the Nidoking. Could find much on this one, though clearly people went berserk for it to have that name :P
- Omastar. Since the Helix Fossil cannot be tossed, it wasn't one of the many valuable items that got accidentally tossed, and miraculously it made it and actually got revived into an Omanyte. Explains what the "praise the Helix" is all about.
- AATTVVV the Venomoth, who was often seen as the weak part of the team. However, it somehow managed to stall a Dragonite to death with PoisonPower.
- AIIIIIIRRR the Lapras. Like Nidoking, couldn't find much info on it, but looking at Bulbapedia. It was an even lower level than Venomoth at just 31, so I can see it being another weaker part of the team.
- aaabaaajss the Pidgeot, who was seen as the team's saviour due to how overlevelled it was. Pretty sure this is what that "Bird Jesus" stuff is all about.
In the PC
Nidoran, BKKBBBBCBB the Venonat, ABB-??AAJJ the Zubat, and Drowzee. Couldn't find much info on them, though I guess they were the lucky ones that didn't end up released.
Just a level 50 Gastly, who, once again, I couldn't find any info on.
The released ones...
I'll start with the noteworthy ones...
- ABBBBBBK( the Charmeleon. That's right, they released their starter.
- Flareon, the one who got have for simply existing. Nobody wanted the Flareon, so when it ended up released, it spawned loads of memes.
Now the others...
- Zubat and x, the two Zubats.
- A, B-!), and Venonat, the three Venonats.
- Nidoran, AAEWWW, H and a, the four Nidorans.
- JLVWNNOOOO the Rattata, CCC the Hitmonlee, AIA the Exeggcute, AAA the Paras, x(araggbaj the Gloom, DUX the Farfetch'd, Geodude, AAJST(???4 the Raticate, and AEWWWWVV the Rhyhorn.
Just a Spearow, who was in an in game trade.
You can find the Pokemon currently in the Crystal stream on the link provided earlier. TheJWittz also has a video on the best moments in the Red stream, so check that out if you're interested, as it may help.