Are you playing with the Diplomacy expansion?  If you are not playing with Diplomacy, I'd advise you to refuse to play with unlocked teams, especially if these players are known to gang up and fight 3v1's.

If you do have the diplomacy expansion pack, I'd recommend limiting the number of winners to 2.  This means that it's very risky for them to form a 3-player alliance, since one of the three will necessarily be betrayed.  Without limiting the number of winners, any unlocked team game will quickly just devolve into one large team forming and beating the crap out of the "odd man out".  That's just not fun, and personally I'd refuse to participate in such a game.

If they rush you, no.  Fortunately, on such a large map a rush is probably not feasible.  Just make sure you have higher-tech units by the time the real fighting starts.  TEC's advantage is primarily early game, but late-game they are very disadvantaged against Advent, their only real edge being a superior economy.  If you can reach 2000 fleet supply, then no TEC player should have any hope of beating you alone.

If the opponent is primarily Javelis LRM and Flak Frigate, you should focus on Destra Crusaders, Iconus Guardians, and the Progenitor Mothership.  This combo works quite simply; use the shield projection ability of the Iconus to absorb incoming damage.  Use the Progenitor's shield restore to replenish your Iconus Guardian's shields.  If the enemy starts focus firing on your Progenitor, use the repulsion ability to push them away and give your progenitor time to recover its shield reserves before moving it back forward.  You may need multiple Progenitors to keep solid coverage.  A destra-based fleet like this can easily rip through a low-level Javelis-based fleet.  If you want to be really evil, swing a guardian behind their lines and if they try to retreat use repulsion to push them back into your fleet's jaws.  Good capital ships to complement this are the Rapture Battlecruiser (vertigo reduces the enemy damage output further, making it easier to recover shields) and the Halcyon Carrier (telekinetic push is a great way to keep bombers off your back, and energy amplification boosts your damage greatly).

If you do find yourself greatly outnumbered, don't be afraid to use starbases.  The Advent starbase has a great ability called "meteor control" which can bombard large forces of enemies with massive meteor showers.  Any large force that gets in range will be destroyed.  This will force the enemy to attack with bombers or uplinked Ogrovs. 

If the enemy turns this into a strike-craft war, then don't be afraid to use the concentration aura of your Rapture battlecruiser to boost your carrier power.  Combine this with multiple Halcyon Carriers to keep the skies clear with their telekinetic push ability, and you're in business.

This won't win a 3v1, but if you play it right, late-game Advent can win a 2v1.

    Ouch!  You definitely need to try eliminating, or at least, crippling, one of them early on in the game.  The TEC is unstoppable in late games, due to its impressive economic system.  The best way to beat a TEC player is to cripple the economy.  My favorite faction is TEC, and I know it pretty well.  If I can stay on my feet early in the game, then I usually can wipe out anyone during a late game play.  The Advent is pretty tough; I’ve played as them too.  If your enemy is focusing on Javelis and Gardas, then you should pick close range sluggers like the Destra.  Neither the Javelis nor the Garda is built for in-fighting. 

    Sovas are my all-time favorite capital ship because of their classic looks.  However, they can also be pretty mean fighters later in the game.  At no time should a Sova be taken lightly, however, if it is at all possible, eliminate the Sovas early on as they become insanely tough later in the game.  The Advent carrier capital ship (Halcyon) is nice, and you should invest in it, however, make certain that you purchase some heavy brawlers.  The Dunov might be able to duke it out with one, but the Sova never could up close.  Basically, it sounds like you have a long-range, anti-fighter enemy.  Focus on high hit points and sheer brute strength.  Run your ships in close, and then rip them apart. 

    As for 3v1…  Good luck!  If these guys are known for teaming up, then you’ll probably have a hard time keeping them apart if they’re friends.  If they are not friends, but only playing acquaintances, then you probably stand a better chance.  I would focus on weakening one of them to the point where it would be a drag on the other two to support him.  If you’re lucky, this might create some internal fighting between the three, and could result in a bit of natural selection.  It would just be 2v1 then…

    Basically, nail their economies.  Disrupt their trade routes.  Focus on firepower and longevity.

    Darvin3 has great advice.  The Rapture and Halcyon capital ships are excellent choices for this situation.  Basically, you haven’t a prayer with three enemies, but you could probably manage two if you were careful.  Divide and conquer.  I personally like to use a fade-and-hit technique where I use two or three capital ships per fleet, and then use a bunch of frigates and cruisers to support them.  I can make a half-dozen or more of these fleets, and I use them in pairs.  I’ll have one trail the other a gravity well behind and use it as support.  If I jump my aggressor fleet into a heavily defended well that I can’t win (even with both fleets), then I’ll jump out.  If I’m lucky, then I can also get my enemy fleet to pursue me right back into the jaws of my second fleet.  This is a nice way to whittle down the odds and make gravity well easier to take.  Also, don’t position a strong fleet on your fringe worlds.  If you keep a light one on the rim world, and it’s scouted, then you can fool your enemy into thinking that it’s lightly defended.  I favor a strong fleet conspicuous on one side of my empire, and a light fleet on the other.  If I think that my light fleet’s world is being scouted for attack, then I’ll often make a thrust on the other side of the map.  This makes it look as though my focus is on one side of my empire, and can spur an attack on what appears to be a weakly defended world.  Once the enemy has jumped into that world’s gravity well and actively engaged my defenders, then I jump my reserve fleet into the well and proceed to shred him.

    Basically, just look for ways to narrow the odds.

Once finished this weekend hopefully...thought Sins can last forever and a LIFE time. Battle report anyone?