So the Faction War leaves everything open, everything up in the air.
We really need to write down some possible plotlines regarding this chaotic time that follows immediately after the war, as well as when things get settled a bit.
First of all, the Factions. They are clearly not gone from the scene, although they are no longer official within the Cage. Some of them already have roles (as told in the FW book), like the Bleakers (who basically change very little) and the Dustmen (who might become the core of a new Undertaker's Guild), while others have shifted focus from the City of Doors onto the planes (such as the Doomguard, whom I find extremely exciting, now that there is nothing holding them back).
Clearly, most of their members aren't about to just give up their beliefs, although they might be looking into other opportunities now. They might try to influence Sigil behind the scenes now (some of them might form guilds). Others might try to push the limits of the Lady's ban on factions.
Ideas include the Harmonium renting their services to the rather inept Sons of Mercy (or even the Sodkillers), the Sensates forming an Entertainer's Guild (to maintain some sort of legitimacy), and others might try to subtly sabotage both the old and the new who try to assert their presence (loads of plotlines here, the Anarchists, the Fated and all the usual suspects are likely to be major players in this).
Of course, now that they are ousted from Sigil, many might try to gain some influence in other places, particularly those that give them access to a lot of planes (such as the Paths, discussed in the previous thread). They might try to expand their presence in their "home" plane - Like the Harmonium trying to work with the Planes-Militant to really start that lawful holy war in the Upper planes (see later thread), and the Mind's Eye trying to take over the old home bases of the Godsmen and the Signers.
The Athar, in particular, must be really desperate. Desperation leads to conflict, and we might see the Athar split across the agnostic-atheist rift, and even some of them joining more extreme splinter groups, such as the Godslayers or the Brotherhood of Belief (the eaters).
No doubt the "winners" of the war, the Anarchists, will wish to keep themselves occupied so they don't start cannabalizing themselves, like trying to prevent the sects gaining influence in the Cage, and moving on to other planar powergroups.
Secondly, we have the guilds. They used to be a real power in Sigil, and it seems very likely that they would form the new government. Sooner or later, the Sigil Advisory Council (headed by Rhys, and heavily influenced by the Ciphers) will have to give up their control. One suggestion is that the new government would consist of newly elected Guildmasters, with the Advisory Council leader being a sort of presiding figurehead (elections in Sigil, anyone?).
A short list of possible guilds:
Minder's Guild (formed by the Sodkillers)
Lawyer's Guild (formed by "ex-Guvners", but probably heavily influenced by the leaders of the Fortress of Enlightened Discipline)
Sanitation Guild (somebody has to take care of the trash, now that the dabus are slacking)
Trader's Guild (a really interesting one - probably very powerful, but hugely conflicted, with such groups as the Merkhants, the PTC and characters such as Shemeska and Zadara fighting over the controls)
Entertainer's Guild and/or Artist's Guild (started by Sensates, HQ in the Civic Festhall)
Craftsmen's guild (ex-Godsmen and others)
Teamster's Union (always important, but after the Storm of Portals, now more than ever)
Undertaker's Guild (Dustmen and collectors)
Worker's Union (possibly started by an Indep)
Prime's Guild/Union (laughable, but we need comic relief too)
Alchemist's Guild
Mage or Warrior's Guild ? (might be inappropriate for the setting, but perhaps you bloods have some ideas for something similar yet more consistent with the planar theme)
Thieve's Guild (funded/started/controlled by a fiend. Cosa Infernis, anyone? Competes with Shemeska and such in the Hive/Lower Ward)
Clerk's Guild
Cleric's / Spiritual / Temple Guild (this group would be extremely powerful, but ultimately splintered. Noshteroth of the Umber Scales was mentioned as a good person to start such a guild, since he is used to running a temple of many power - abyssal lords, no less)
And finally, we have the sects that would move in, seeing opportunity.
My favorites are the Ring-Givers, who would definitely be playing a larger part now than ever. This might be the right time to move Jeremo the Natterer, the Lady's Jester, to full sectol-hood, and switch their focus to the City of Doors. They would be real players in the wake of the war, giving (and of course, collecting) favors in order to soldify their influence. The Jester's Palace seems like a good place for them to start out, and perhaps Jeremo, known as one of the richest of the golden lords, could buy out some old faction HQ, such as the Hall of Records, for their use.
The Planes-Militant are another sect that might increase in influence, but perhaps they are better used for another plotline, regarding the (cold) war in the upper planes. See next thread.
Tons of other sects should be moving in, making Sigil even more interesting than it ever was. Ideas?
There may be a nice expansion of organised crime through every part of the City. Several syndicates or just gangs might fill in the hole the Harmonium/Mercykillers left, since the Guard doesn't seem to perform very well. I also don't see why the "big guys" (like Shmenskar) should be interested in those.. minor affairs (as long as they are), since they are, well, minor affairs to them. This should leave much space for criminal activities without getting involved too far in things you don't want to be involved - everyday life in Sigil is "exiting" enough without this. 
The Sodkillers actually make a lot of sense; after all, many of them were trusted Harmonium allies before the Faction War. They're a well-armed, capable group, and their allegiance to Law and Justice should still be strong; at least as strong as that of the Sons of Mercy, who might be perceived as wishy-washy compared to the Mercykillers of old, more concerned with letting criminals off the hook than justice. Could there be a Willie Horton of Sigil to inflame sentiments against the Sons of Mercy and to the Sodkillers' favor? That could be an adventure there.