This is the eternal thorn in the side of every attempt to make a Stargate mod that's come along - the way tactics work in both universe is completely different. So here's a thought:
The Ori, having recently arrived in our galaxy and wanting to maximize the value of their supreme naval advantage, releases some Ori superweapon or another that shuts down the entire stargate network throughout the Milky Way. All of 'em. This results in a scrabble amongst the planets capable of producing starships (i.e., the faction homeworlds) to expand to other worlds by naval means. We'll just ignore the sandbox games where the Ori do not appear.
EDIT: Some possible descriptions for each race. Note that I use lower case nouns to describe species, and upper case nouns to describe factions within a species (for example, "human" but "Tau'ri", and "symbiote" but "Goa'uld")
The Tau'ri
Leader: Jack O'Neill
Homeworld: Earth
Tau'ri means "Those of the First World", and the Tau'ri do appear to be the oldest of all human civilizations. Inhabiting the planet on which humanity originally evolved, the Tau'ri have only recently regained access to the Stargate network, but by defeating the Replicators have proved themselves to be a formidable player on the galactic stage.
Free Jaffa Nation
Leader: Teal'c
Homeworld: Chulak
Emerging from the ashes of the reign of the System Lords, the once-enslaved Jaffa have banded together to form their own, democratic nation. The recent death of Council Leader Gerak and the capital on the planet Dakara has crippled the Jaffa, but the former leader of the Jaffa Resistance, Teal'c, has stepped forward to take command.
The Tok'ra
Leader: Per'sus
Homeworld: Unknown
Begun by the symbiote queen Egreria, Tok'ra translates literally as "Against Ra" - they began as symbiotes who disapproved of the treatment of humans and unas by Ra and the Goa'uld, and banded together to form a resistance. The Tok'ra have benefitted from their alliance with the Tau'ri, but many in the council distrust their former allies.
Goa'uld Empire
Leader: Ba'al-014
Homeworld: Unknown
Though the destruction of the High Council of the System Lords has shattered the Goa'uld's strength in the galaxy, those that remain now answer to a single being - the fourteenth clone of the System Lord Ba'al, who has become independant of his original creator. All Goa'uld are selfish and megalomaniacal - the name means "Children of the Gods" - but in this time of desperation they have banded together.
The Asgard
Leader: Commander Thor
Homeworld: Cimmeria
Once charged with enforcing the Protected Planets Treaty, the Asgard were drawn out of galactic affairs by their conflict with the robotic Replicators. With the Replicators defeated, they have moved on to the issues of the Goa'uld and the Ori. From the planet Cimmeria, they seek to rebuild their empire in the Milky Way, and hopefully defeat the evils that plague it.
Lucian Alliance
Leader: Unknown
Homeworld: Unknown
As the power of the Goa'uld started to crumble, something had to fill the gap, and the Lucian Alliance was only too happy to oblige. An immense, interplanetary "trade federation" spanning the galaxy, the Alliance has no regard for morality or legality - it is really nothing more than a glorified mafia.
The Trust
Leader: Ba'al
Homeworld: Unknown
Originally an illicit organization within the Tau'ri's NID, the Trust were eventually banished from Earth altogether, and subsequently infiltrated with the Goa'uld. When Ba'al lost control of his offworld empire to his clone, he left Earth and began to build the Trust into a credible power. He now stands ready to regain his position in the galaxy.
The Wraith
Leader: Michael
Homeworld: Unknown
Evolving in the Pegasus Galaxy as a genetic cross between humans and the parasitic iratus bug, the wraith resemble vampires, forced to drain the life from humans merely to maintain their own existance. A retrovirus exists that can transform wraith into ordinary humans at the expense of their memory, and most of the wraith that have come to the Milky Way have undergone this treatment. They seek nothing other than to rebuild their race away from its past in Pegasus.
The Genii
Leader: Ladon Redim
Homeworld: Unknown
The Genii may not be the most advanced society, but they are masters of deceit. They acquired, through treachery, the keys to constructing a nuclear missile, and the Ancient starships known as "Puddle Jumpers." It was only a matter of time before they acquired the plans to the intergalactic hyperdrive, and set out to create their own empire in the Milky Way.
The Asurans
Leader: Oberoth
Homeworld: New Asuras
The Asurans are a mechnical race, created from nanite composites. They resemble their creators, the Ancients, who in turn resemble humans. However, the Asurans are nevertheless unable to coexist peacefully with humanity. Aggression is written into their very nature - they were designed as weapons of war, and they cannot override that origin.
Anything labeled as "Unknown" needs suggestions. Also, Oberoth may well be dead (Michael also could be, but the manner his "death" was handled suggested that he escaped) so we need to figure out who the new leader of the Asurans would be in that case.