Hopefully everyone gets what I mean by that. Generally, these teams are easy to spot forming, as they have 1 member with CC that will group up the enemy (Galio, Orianna, Amumu), 1 member who is tanky with an initiate (Garen, Amumu) and then just a whole bunch of nasty AOE powerhouses to round out the combo like Brand, Annie, Lux, Ez, MF....

These comps absolutely wreck teamfights by blasting away two, three or as many as all five enemy team members in the very first few seconds. Even before ranked, I seem to be running into them extremely often and I'd like to know, what are good ways to counter a strategy like this?

Is it as simple as avoiding team engagements altogether, or sacrificing the least-fed member of the team to try and draw the combo solely on themselves (since they almost always rely heavily on ults)? I've also considered that a single hypercarry with the ability to make themselves invulnerable/untargetable might work, something like a heavy AP Yi, Tryndamere or even a Fiora, with her ult.

More experienced strategiests, what would you say? It's not hard to see these sorts of combos coming, so how do you go about building/playing to counter them?

well, you can counter some of this in team select by getting someone who can't be bursted as the AP mid (cho is great for this, also Morde to a lesser extent). Kayle's ult would be great as well.

the problem with burst teams is that they are fragile. Tanky bruisers will wreck them (Darius, Jax, J4, Etc.) After that, it's all team work and not feeding their carries

I wouldn't call these super nuke so much as aoe synergy. The answer is just positioning and delayed counter initiation if you're a carry.

there are a few ways to deal with it.

-run a pick comp (pick off someone to lessen the power of their wombo combo)
-split push comps played well prevent 5 vs 5 fights and take objectives (probably the best option in solo que)
-run an aoe wombo combo comp yourself (whoever gets the right engage first wins)

Ashe is hilarious for preventing aoe wombo combos because she is excellent at picking off opponents from afar or just generally stopping 1 member of the aoe comp long enough to create a numbers advantage for your team. Other options include Lux and Xerath.

Champs like Gragas, Cho'Gath and Janna provide heavy disengage/peel and fight resets that allow for your team to reposition themselves to deal with the layering of aoes.

It goes without saying but proper ward coverage can prevent enemies from engaging on you and allow you to make plays by avoiding 5 vs 5s and taking objectives. The other important thing to keep in mind is ultimate timers. Typically wombo combo comps wait for 5 ultis to be up for full effectiveness so make sure you keep track of them. You can sort of half ass it by remembering whose ulti CD is the longest but outside of team play people love to blow cooldowns without fully assessing the situation.

During this downtime it is imperative you make your move. Your best opportunity is when the enemy team blows their CDs but fail to take an objective. Now you can force fights without worrying about them stacking aoes.

You beat AoE comps by split pushing. Most AoE heavy champs aren't so great at 1v1, and the strong split push choices should be able to solo anyone that comes to stop them. If not, it weakens the combo for each person you can draw away from the main group.

Failing that, spreading out, and/or quicksilver sashes can greatly mitigate the pain.

Awesome. I have tried the split pushing idea against teams like this, but the problem I've run into has been that often, certain key elements of the Wombo Combo and split off to deal with a single split pusher (example: Garen and Oriana can head off and deal with whoever they want while the rest of the team can stay and fight)

Thanks for the pointers, though!

Poke comps work great against AOE Comps.

Poke champions:
Nidalee
Lux
Gragas
Xerath
Ahri
Jayce
Sivir
Ziggs

Certain Champions are extremely good at just preventing those AOE engages, or lessening the damage:
Zilean (He can speed the person out of position, ult them, or severely slow the engager.)
Kayle(That ultimate can keep the carry from being blown by their burst)
Trundle(That dirty *****!)
Anivia(That Wall! Also has nice aoe of her own.)
Thresh(Lantern, his ultimate is one hell of a dirty disengage.)
Nami(Great disengage)
Janna(Great disengage)
Karthus(Passive OP)
Gragas(Disengage)

the splitpush tactic involves 1 of two things (if both occur you probably won the game)

-the splitpusher (ie: nidalee, singed, shen) get fed
-the splitpusher has teleport

in your example if orianna or garen came that puts everyone else in a 4 vs 4 so your options are:

-if youre fed you can duel garen or orianna
-if you have tp, keep pushing until the very last moment and tp into the fight while the person who came to deal with you ends up behind
-if no one comes to deal with you then you got an objective and all your team had to do was hold off the fight provided everyone is on an equal footing

as you can see you need to be a worthy threat if you split push and you will need assistance to get rolling (unless you beat your lane opponent solo)

the mentality of this is that you are able to duel anyone. if someone comes to handle you, you either kill them and take the objective, or take the objective while you team holds them off. sometimes this strategy requires you to trade objectives but as you do it more you get a feel for priorities.

Split-pushing works. So, too, does a poke comp with particularly good map vision thanks to wards (as Sephiroth stated). If you can poke them down before they burst you disincentivize a large engagement. Forcing one or two members to back or die basically shuts down an AoE team comp.

Great champions that technically could work in either composition are Mundo and Nidalee.

Another thing to consider is to have your AP carry build a Zhonya's. That item is a get out of jail free card when an AoE comp chooses to blow it's load on your APC.

Mostly, you want to take away their ability to run teamfights on their terms. Frequent ambushes, a lot of wards/map awareness, and a good poke composition can work well toward this end.