Besides putting Light Screen on Chansey or Starmie, the best methods I've found to neuter the crab are to put Kinesis on Zam or Leech Seed on Egg.
There are, of course, a lot more ways to kill it than to wall it.
Hit it until it dies. Or bring out Slowbro if you want to force the issue.
Reflect snorlax
Amnesia snorlax
Well, that all depends on what its attacking moves are. Slowbro can generally do pretty well, though.
The only true counters to Dragonite are Cloyster and Lapras. Other than that, just don't let it set up and punish it for Hyper Beaming.
Egg. Only does it a few times, though, so if you really want to neuter it, put recovery moves (Mega Drain, Leech Seed, Rest) on Egg.
Starmie and Slowbro aren't terrible either.
Switch in to snorlax
Switch in to tauros
Cloyster, unless they have Thunderbolt. If unknown moveset, Slowbro's probably the safest.
lol.
That's all I can think of at the moment.
Zapdos - I think we all know the counters to that.
Starmie - See Zapdos.
Hyper Beam - you need a way to punish predicted Hyper Beams. Rhydon's the best, but a fresh Dragonite can also work.
Many of those are easy to counter, but not all at the same time. I'm having trouble thinking of a team that has a solid counter to all of these threats whilst still maintaining decent offence.
I've played around with this sort of thing myself. Best I can think of would be something like this:
Lead: Alakazam. It'll either get slept or paralysed, but Alakazam's the most defensive lead.
Exeggutor: With Leech Seed + Rest, it holds off Slowbro and Rhydon quite effectively. Season with status and attacks to taste.
Cloyster: Counters Dragonite and Snorlax, and additionally gives you a totally safe switch-in to Ice Beam or Blizzard. Its existence can also make an opponent think twice about Hyper Beam.
Chansey: It's Chansey. If you didn't put Sleep Powder on Egg, put Sing on here. Otherwise, putting Reflect on gives you a solid Zapdos wall.
Snorlax: Body Slam, Selfdestruct, season to taste. You need something that can explode in a pinch.
Slowbro: Big scary offensive threat. Also gives you something that can switch into, and paralyse, basically any other offensive threat.
Well, that's my best attempt, anyway.