Alright, I tried to do my homework and look through every page of this thread. I basically scanned it to see what I was specifically looking for. If I missed some posts, I'm sorry. Here are my parties, and I'm sorry if this isn't exactly what this thread is supposed to be about.
Squirrel Party -
Riou, Muku, Maku
Meku, Miku, Moku
I think I did see someone comment on the hilarity of this party facing the beast rune. You don't have to tell me that it wouldn't be the ideal party in terms of battle, but it would be hilarious. And if you can actually beat the beast rune, without glitches, tricks, or cheats, you would be a brilliant strategist.
Beast Party -
Shiro, Feather, Sigfried/Abizboah
Same thing as the last one: not the ideal party in terms of game stats. However, why not have a group of beasts beat up on the Beast Rune. I actually have beaten the Beast Rune with this party before. It's slightly amusing to see the 'dialogue' when you have four characters in your party who can't ('don't' in Riou's case) talk.
Ultimate Power -
Sierra, Pesmerga, Viktor
Riou, Luc, Tir
If I remember correctly, according to KFCrispy's and RedKilley's posts, all of these characters are great characters in terms of game-battle mechanics. So, this would be the one battle party that I have suggested that would make sense if you want the most capable party and want to defeat the Beast Rune quickly instead of just an amusing or profound party.
However, the reason I like this party is for story reasons. This should be a group of companions that could almost never be defeated. You can only use the power of two of the true runes in the game (Soul Eater and Bright Shield). But if this were real Suikoden life, and they were about to die, almost any one of them could unleash the power of their rune and blast everyone away (like True Fire, True Water, Punishment, Sun explosions). For gameplay reasons, we can't use the full power of the True Runes, especially Night, Blue Moon, and Wind. But surely they have the same raw power that some of the others have displayed.
However, there is one group of enemies that could pose a serious threat to this party. This group would probably never assemble (since a couple of them hate each other already), but it could be a deadly group of foes:
Hikussak(Circle), Yuber(Eightfold), Barbarosa(Sovereign), Luca(with the Beast somehow), Sasarai(Earth), Windy(Gate)
For the most part, all of these characters are firmly ensconsced as enemies. (Luc and Sasarai obviously change places, but since this is SII, Luc is a good guy and Sasarai a bad.) Not only that, but they're the main bad guys. Even further, this breaks down into excellent one-on-one duels. The ancients: Hikussak vs. Sierra. Yuber vs. Pesmerga (the last I heard, no one knows if Pes has a true rune or not. No matter, he is still supernatural). Barbarosa (Dragon King Sword) vs. Viktor (Star Dragon Sword). Luca vs. Riou (Here, Jowy would have to be brought in to team up against Luca if he had the Beast Rune somehow affixed to his body or sword. Maybe Jowy could stab him in the back again with the Black Sword.) Sasarai vs. Luc (Obvious). Windy vs. Tir (Once again, Obvious).
If Hikussak could get along with Windy and Yuber and vice versa, and these two groups met on the highway between Muse and Greenhill, those little squirrels better fly the heck away in a hurry. Luc and Yuber might've gotten their wish of destruction and chaos 30 years sooner.
Once again, I'm sorry if I was supposed to provide individual reasons for the members I picked. While there are certain characters that I just absolutely don't use, most of my parties are chosen because of some relationship they share with the other characters (that doesn't have to be Unite attacks), not because they are the absolute best at what they do. I figure that I can beat the game with just about any party; I'm playing for the story, even if it's just my imagination writing into the story.
If there are any other funny parties or profound parties, I'd love to see some more of that.