Articuno, Zapdos, and Moltres will be appearing in tier-5 max battles. This post will help you choose effective counters and strategies. It's aimed at people who want to tackle the boss with a single group of 4 trainers, but the tips apply even to much larger groups.

TL;DR:

• Against Articuno, back out against Hurricane (unless you're using just Excadrill, in which case Blizzard is the scarier move). Excadrill offers many routes to victory on its own, despite being only middling defensively. Alternatively, you can combine excellent tanks (Lapras and Blastoise) with strong max-phase attackers like G-Toxtricity, fire (G-Charizard or Cinderace), and steel (Metagross and Excadrill).
• Against Zapdos, you won't need to back out against anything if you use Excadrill as a tank. Use G-Lapras, G-Gengar, or your brand-new Articuno as max-phase attackers.
• Against Moltres, back out against Overheat and maybe Fire Blast. (That's 70% of all battles, a lot of backing out!) Run G-Blastoise both defensively and offensively, using one of your three max moves for healing on each max phase of battle if Moltres is using Sky Attack.

This analysis assumes you're using level 35 counters with max moves at 2. It also assumes a boss CPM 0.765, HP 50000, and 8.5s between attacks. Some of these are guesses, so treat the conclusions with caution. UPDATE: the parameters are way different than expected: the boss does much more damage but also has much lower HP. The gap of 8.5s between attacks seems roughly correct, give or take.

(EDIT) One interesting general point: while it's good advice to avoid using your charged move against a G-max boss, there's a chance that using certain charged moves might make sense against a T5 boss. Specifically, if the guess of 8.5s between attacks is correct (and it may not be), then as long as you charge the meter in less than 17s, you will likely sustain only one boss attack per cycle. Since a 0.5s fast move charges the meter in 12.5s if used exclusively (assuming a group of 4), there should be enough time to sneak in one or more charged attacks each cycle, where the number you can afford to use depends on the charged attack's cooldown. In the analysis below, Inteleon against Moltres appears to win somewhat more easily by using Surf, a 1.5s cooldown charged attack, alongside Water Gun as a fast move. Again, keep in mind that this depends on the gap between boss attacks (currently unknown), and also on the details of the timing of enragement (currently poorly understood, at least by this author), specifically whether the duration of the max phase of battle counts against the enrage timer (here I assume that it does not).

Articuno

Counters for Articuno. Top: defensive info. Middle: \"raid-like\" DPS using charged attack. Bottom: fast-only and max-attack

Articuno will be the easiest of the three by a fair margin. Hurricane is the only move that will be difficult to handle, and even there Metagross, Excadrill, and Lapras lose less than a third of their HP from a single strike. Since both Excadrill and Lapras can charge the meter while taking no more than two boss attacks, even Hurricane can be survived. Still, given that two-thirds of the time the boss won't have Hurricane, it's easy to back out and hope for a more favorable combination of moves on the next try.

Great defensive types are Lapras and Blastoise, both of which charge the meter quickly with 0.5s fast moves while being able to tank most or all of Articuno's moves. (Metagross also has good survivability, but it charges the meter more slowly.)

Great offensive types are G-Toxtricity, G-Charizard, Metagross, Excadrill, and Cinderace.

Recommended strategies:

• ("tank") use Water Gun Lapras or Water Gun Blastoise as a tank during the normal phase of battle, and switch to a strong attacker during the max phase.
• ("sustainable") If everyone fields a Metal Claw Excadrill with both max attack and max spirit at at least level 2, you may be able to win without losing a single pokemon. During each max phase, use 1 of your 3 max moves for healing. Don't use your charged attack, or at least not more than once (and only if you can sneak it in without taking a second boss attack). This probably won't work against Blizzard, but it seems likely work against anything else. This strategy may require having your max attack at level 3, it depends on how high Niantic sets the boss HP.
• ("raid-like") a group with 12 level 35 Excadrills seems likely to be able to win by using both Metal Claw and (perhaps surprisingly) Rock Slide with no fancy strategy required and no shielding or healing during the max phase. I estimate that each trainer will "go through" 2.8 Excadrills and win in about 150s of cumulative normal-phase battle, well before the enrage timer kicks in. You can therefore afford to use some healing, if you want to increase survivability at the cost of prolonging the battle. If you plan to use healing, you may be better off avoiding the use of Rock Slide so you charge the meter faster.

Zapdos

Counters for Zapdos. Top: defensive info. Middle: \"raid-like\" DPS, using charged attack. Bottom: fast-only and max-attack

Zapdos is intermediate but not that much worse than Articuno. Zap Cannon is the hardest move to handle. However, Excadrill resists every one of Zapdos' moves, and even the fearsome Zap Cannon does only about 25% damage to Excadrill. If you use Excadrill defensively, you can probably handle any combination of boss moves.

While Excadrill is hands-down the best defensive type, Venusaur and Rillaboom (using Scratch) are other great options that also charge the meter quickly; just make sure you swap out without taking a hit from Drill Peck. As often happens, Metagross can tank most moves (Zap Cannon excepted) but charges the meter more slowly.

Attack-wise, the champion max-attacker is G-Lapras, closely followed by G-Gengar. Articuno (which you may have by the time Zapdos comes out), Cryogonal, and G-Charizard will also be good choices. Unlike Articuno, none of the good attackers are even reasonable defensively, so Zapdos is a boss for which "tank" strategies are your best choice.

Recommended strategies:

• ("tank") use Metal Claw Excadrill during the normal phase, and switch to a strong attacker during the max phase.
• ("tank 2") use Venusaur or Rillaboom at a tank, backing out if Drill Peck is among the boss' moves. If you're comfortable with fast-swapping, you can also throw in Metagross as a tank to handle Drill Peck.

Moltres

Counters for Moltres. Top: defensive info. Middle: \"raid-like\" DPS, using charged attack. Bottom: fast-only and max-attack

Moltres will be the scary beast among the three. While it's defensively vulnerable to quite a few counters, its attacks are fearsome: Overheat and Fire Blast do at least 40% damage against even the best defender against them (Blastoise), and even Heat Wave is pretty tough on nearly all options. You're likely to have to do a lot of backing out to beat Moltres:

• The boss will have Overheat and/or Fire Blast 70% of the time
• The boss will have at least one of Overheat, Fire Blast, and Heat Wave 90% of the time

Henceforth I'll assume you'll just back out against Overheat or Fire Blast, and try to handle the rest.

Defensively, Blastoise is top-tier, with Sky Attack being the most threating of the remaining moves. This, however, is easily handled by Excadrill and Metagross. Hence, a recommended defensive strategy is to lead with Blastoise but have a steel type for fast-swapping if needed.

Offensively, G-Toxtricity, Inteleon, Zapdos, Kingler, and G-Blastoise are all great.

Recommended strategies:

• ("pure Blastoise") Use Water Gun Blastoise for everything. Unless you're in a large gathering of trainers, you may need to use some healing during the max phase to survive to the end. Fortunately, Moltres is sufficiently weak that you have enough time for some healing: if everyone brings three Blastoise to the battle, and you use only 1 of your 3 max moves for healing, you should win before the enrage timer kicks in.
• ("Inteleon/Blastoise") You can mix Blastoise and Inteleon (best if Inteleon is level 40 or higher). Inteleon's Surf is sufficiently fast (1.5s cooldown) that you can afford to use it without receiving an additional boss attack during the normal phase of battle. Your resulting DPS, coupled with water's resistance to Moltres' fire moves, is so high that you can afford to use slightly over half of your max moves for healing. This suffices for Inteleon to survive long enough for the win.
• ("fast-swapping") Swap between Blastoise and a steel type (Excadrill or Metagross) as needed during normal phase of battle (largely to handle Sky Attack). Use any strong attacker during the max phase. Take occassional cycles to heal if you need to, and consider appointing a taunter to bias the attacks to ones you're better at handling.

EDIT: For anyone tempted to try soloing or duoing Moltres, perhaps surprisingly the best defensive pair is Excadrill/Metagross. Of course you'll need to wait until Moltres is running Ancient Power & Sky Attack, which is only 10% of move sets. Leave Excadrill in most of the time and fast-swap to Metagross if you're about to get hit with Sky Attack. Then swap to G-Toxtricity for max-damage. You should have a little time for shielding (which is preferred over healing with fewer than 3 trainers) if Moltres uses the same parameters as Articuno.