I like to do the solo IC dthrow CG on Sheik and switch to the ledge CG when I can. Properly done ledge CGs should mean death.
If the Sheik is camping hard on platforms, you have a few options. I think the best option against good Sheiks is to stay near the ground and bait Sheik into coming down with a fair. You can't punish it well, but it gets Sheik off the platform and you can now apply stuff I said in post #358.
If Sheik really doesn't want to come down and is just jumping and throwing needles. Try to get under her and uair. Sheiks that play the match-up this way will usually jump to the center platform (I'm assuming we're on the usual three floating platform layout if the Sheik is doing this sort of camping), which can be tough to punish, but is nonetheless a better position for you then her as long as you can stay under her.
On other levels with floating platforms that Sheik can abuse, but no higher platform to flee to once you get below her, a lot of Sheiks will shield, which you can punish with waveland -> grab. Some Sheiks will do this even if they can flee somewhere safer. If the Sheik doesn't shield, she'll probably run off to one of the sides to get to the floor again.
A few other miscellaneous notes:
-If you can get Sheik near the edge, take note of what she likes to do: if she rolls or spot dodges, you grab her and kill her from there. If she jumps, which a lot of Sheiks and other characters in general do when near the edge, nair and bair are good for pushing her off. Those are risky, though, and if you'd prefer to stay on the floor, that's fine, too; the worst she can do is waveland onto a platform above you and do a falling bair off the other side, which actually is a pretty scary position, but you should be able to prevent this situation from arising on reaction by heading toward the center of the stage if you see her jump.
-If the Sheik likes to Shino stall, you can wavedash and grab the edge to force her to come on stage and take a hit/grab or stupidly kill herself. A lot of Sheiks will wavedash onto the edge and try to get safely back to the center of the stage if they see you try to do this; fortunately, this is easy to bait. For example, if you're facing towards a Sheik who is Shino stalling and you turn around, your opponent probably thinks you're going to try to take the edge. They wavedash onto the stage and you simply turn around and grab. You could even do a stationary wavedash if you think your foe responds to the "boing" sound the ICs' wavedash makes if you want to scare her back onstage.
-Fair is not reliable in this match-up at all. Don't use it unless you have no alternatives.
-If you have a habit of dsmashing a lot, which many ICs do, try to break it just for this match-up; I used to do this and get punished badly since Sheik can trivially short hop over dsmash. Replacing your dsmash instinct with a usmash one might work alright.
-Don't let Sheik trap you in your shield. It can be tempting to just sit in your shield if you're being pressured, since it often feels like you can't do much against Sheik's wall of fairs, but keep in mind that you can. Don't be afraid to get under her and usmash/utilt.
-I think there was something else I wanted to talk about, but I don't remember. Maybe I'll rant more about this match-up tomorrow.
@choknater: Bthrow is really good in ICs dittos. I think it's the most reliable way you've got of separating your rival inuits. Also, dthrow -> dair usually works against other ICs mains, because who the **** knows how ICs should DI out of other ICs' CGs.
If you can separate the other ICs, your first priority should be to keep them apart. Killing Nana isn't as trivial as it seems with ICs, so I don't think it's usually best to chase after her with bloodlust. Also,since most ICs panic a little when Nana is away, your enemy will probably play dumber than usual and you can exploit this.
Brainstorming:
If the other Nana isn't at a high enough percentage to KO with some random smash, you might be able to carry off the stage with shffl'd nairs and spike her with fair. The obvious threat here is the other Popo, who is still probably nearby; you might be able to do something like have your Nana blizzard and while he is waiting for that to end or doing something to get around it, you could chase his Nana and KO her. I'd be a bit worried about leaving my own Nana vulnerable when doing this, but he'd probably have a hard time gimping or otherwise substantially ****** Nana without his own fine lady.
-I think desynched ice block/blizzard camping might work well against Sopo for the same reason it works on Luigi; namely, ice blocks make his ground approach even more sluggish than it already is and he can't reliably approach from above to punish blizzard since he's also sluggish in the air. I'm not sure how desynching would work against a pair of ICs, though; I'd guess that it would be better to stay synched, as is almost always the case.
-Since ICs suck at protecting themselves below and are really good at protecting themselves from above, it's definitely good to keep the other ICs above you. Since you both probably like being glued to the ground, I'm not sure how often you can take advantage of this, though. Usmash/utilt are really hard to land in ICs dittos and I don't think uthrow is as good as bthrow most of the time. Maybe if you get the other ICs separated, you can uthrow or dthrow -> usmash or something to send the other Popo upwards and harass him from below while his Nana tries to get back to him. Maybe you could even get him to try to get away from your pressure and leave his Nana more vulnerable in the process. It's probably easier to take advantage of this aerial disparity in Sopo dittos.
-If you're edgeguarding Sopo, and he's recovering high, I think its best to let him land and then grab him, unless you're also Sopo, in which case bair/dsmash/something else is probably better. If Sopo isn't recovery particularly high, the fair meteor spike would probably KO him; he almost definitely already used his double jump and his up+B isn't going to save him if you fair him out of a solo squall.
I'm going to sleep.