Help! Computer gang up on me in all vs all

It is tyipcal AI behavior, try working it with teams locked and set groups

Either take Ryat's suggestion and lock the teams, or do the same thing they're doing and start making friends.  If you have a few allies (or at least cease-fires), it's not to hard to fend off the few remaining players who can get to you.  I've played games where most of the map was friendly to me, at least for a time.

The AI doesn't go through the same appeasment process that you will need to do to make them happy (a frequent complaint that should be fixed with Diplomacy soon), but they do make and break alliances throughout the game.  It's how they team up and beat most new human players.  You should try to beat them at their own game.

On a few occasions (that is, infrequently) you may see AIs break their alliances with each other. It usually follows after another AI has been defeated, and since AIs always need an opponent to fight, they choose one of their current allies to go to war against.

I've only witnessed it happen twice in all my times playing Sins, first occasion was when myself and two other AIs were left, one AI ended up utterly destroying the other's fleet, and the second, more recent occasion, the two only fought for about 10 minutes before they made up and became allies again (though this was enough for me to step in and steal a few of the planets they lost from each other).

The problem is that you have to play a map aimed at your skill level, you could defeat seven ai's in an unlocked game before you try nine?.  If you want to play large single player unlocked FFA, I'd suggest Ancient Gifts might be a good map, there are other similar set maps.  The huge single random map isn't really suitable for what you want.   

If you can cope with custom maps, My own Deus Ex Machina is available as a custom download from the downloads section of this site, that would be suitable for single player unlocked FFA with 5 ai.  For regular players just put the map with all the other galaxy maps in the galaxy folder, for Entrenchment you have to add the name to the manifest and increment the total number of maps by one.

Good advice, but another option is to make a map with multiple star systems, and have the first star with one player, and have the other stars with two. That way, they will probably be busy fighting EACH OTHER, and not you; this usually works until they start expanding to other star systems, at which point they might ally, but the two AIs in system B (you are in system A) probably won't ally with the AIs in star C, so you just get a ceasefire with one of them, keep them happy so you keep the cease fire (you should get a peace treaty with one AI,but other than that, don't get a peace treaty, they are harder to break, and when you do, you can't attack for a while, and whatever you do, DO NOT GIVE THEM planet or ship vision, it just gives them battle maps of you defenses for when its just you and them), and then you both attack the the other two AIs, and this is where you can use the peace treaty to use attack pings. Then Once Star B is subjugated, then you stay at peace with the allied AI in Star C, and you both conquer the other AI, and then wait a little while, build up a MASSIVE fleet, then if you aren't back at war already, go to war and go on the offensive immediately. Use superweapons when necessary, the Kostura works best, and you should win pretty quickly 

What I'm doing is holding out for Diplomacy.   There's still plenty of fun to be had with locked teams and unfair AI to last awhile.  Then go to unlocked when Diplomacy comes out.  Although I'm not doing the beta, I can imagine unlocked teams are the star of the show there.  You might never want to go back.

Do their missions, as much as possible.  Unless you are good enough to win playing 1-v-9, you can't ignore the diplomacy aspect of the game (even if you aren't playing the diplomacy beta).

Kill them all.

Impossible, if certain situations arise, such as a destabilization of power that results from the defeat of one attacker which results in a shift of alliances, which results in more fleets attacking your planets.

It's hit or miss.  If they are coming against you just hold out as long as you can.  The thing is that they are against eachother also, so if you can cause damage to others you are bound to satisfy destroy this quests which also gives improved standing.  Use that to get them offering cease fires or alliances.

OR, you could give in to their demands w/ skilled diplomats tech for TEC, and offer them cease fire and break it when necessary