Characters with good synergy in ME3 Multiplayer

Reave and Warp make an awesome biotic combination. Both detonate each other and casting animation is fast.

Pick one character with Reave & one with Warp and you'll be detonating each others powers every 2-3 seconds.

That being said, the maximum biotic explosion damage comes from Warp+Throw & Warp+Shockwave combinations (sources below). Throw is arguably the best detonator power as it has a very fast recharge and detonates on all types of (what's the word for this? protection?) i.e. health/shield/barrier/armor.

So if the team has more than 2 players, equip one person with Throw and others with Warp/Reave/Dark Channel. Now the person with Throw has only one thing to do - spam the key that throws Throw, detonating every enemy in front of the team. (This is team-work, the team will need to stick together).

If there are only two biotics in the team, I'd suggest to go with Warp+Reave combination which is more reliable as Throw can only detonate and not initiate a biotic explosion.

Maximising biotic damage

Biotic explosion damage depends only on the ranks of the power and on nothing else not even from power damage bonuses (through some powers can be modified for extra combo damage, see source below). So ensure that the powers that you are using for biotic explosion are on Rank 6.

PS: Equip yourself with Acolyte, for the only place where biotics fall a little short - shields.

Sources:

1. Mass Effect Wikia: Power Combos
2. Bioware Social Netowork: Gameplay Data & Mechanics
3. Bioware Social Network: Combo Damage Calculation
4. Google Spreadsheet: Combo Damages
5. Mass Effect Wikia: Acolyte

N7 Destroyer + N7 Demolisher.

Where Destroyer is specced for Devastator Mode & Multi Frag Grenade, while Demolisher's Supply Pylon is maximised for ammo & grenade production, thus ensuring that ammo supply to Destroyer's Harrier & grenades never ends.

Add third player as Volus Engineer to the team with his Shield Boost maxed for restoring allies' shield and the Destroyer is an unstoppable juggernaut.

Add fourth player as Asari Justicar to the team with her Biotic Sphere maxed for protection and the Destroyer is [someone should edit the post and fill something clever here].

Important note: Since all characters are mostly in support role for the Destroyer. The Destroyer needs to ensure that he is maximised for Damage per Second (DPS) by using Ammo/Weapon/Armor consumables & Gear along with good weapons and appropriate weapon mods.

PS: Two N7 Destroyers with two support characters (with at least one of them being N7 Demolisher and another being a Volus Engineer or N7 Demolisher) will wreck havoc to the battlefield.

You've already covered many biotic combinations, here are a couple of tech ones that might be of interest to anyone who happens upon this question:

(1) Snap freeze (N7 Paladin or AIU) and any character with chain overload (Human eng, Turian sentinel, Turian Ghost, Geth eng). Snap freeze works through walls and primes everything for 2x damage cryo explosions.

(2) Any character with flamer and any character with chain overload. Flamer will prime multiple enemies for fire explosions which do great damage against armour. In addition setting off fire explosions on bosses can sometimes help to take out lesser units in proximity.

Why is overload such a great detonator? It's hitscan and with one or both of the chain evolutions you can get multiple explosions per cast. In addition the overload damage is applied before the combo damage and as it's so effective at removing shields or barriers the combo damage will often hit enemy health/armour.

Here's a good video about combo explosions: