I'm notoriously bad vs ICs but I have some ideas.
The below is basically how I manage the ICs MU right now. I'm not sure whether it's right or not. Open to suggestions.
When I play against characters I don't get much experience against, I think about what position they're weakest in and how I could possibly go about creating a style that sets up that position. I also think about what I want to avoid in the MU and what that requires I do. Then I marry the two strains of thought and see what I can come up with. Beginning with the former, I know from basic analysis and talking to Fly Amanita that ICs are weakest at the edge, in the air, and on platforms. Since they are going to effectively glue themselves to the floor whenever possible, the MU is mostly played as a pushing and retreating game. Periodically Sheik will be forced up to platforms to regain footing (because Sheik will sometimes be pushed back because she really has no business challenging certain things like the blizzard wall).
What I want to avoid in the MU is basically being hit by anything that could possibly lead to grab. For this reason, I think low aerial (SHFF Fair AC being the big one) is the foundation of everything you want to internalize in the MU. It's safe, effective, and (when done correctly) unpunishable by grab. Sheik is squishy in this MU so you don't want to get hit. In order for them to counter the spaced fairs, I think they're probably going to be fishing for shield grabs (which shouldn't work, but it will work if you're not doing them correctly and ICs generally like to toss out poor shield grabs [even at high level]), crouch punishes (including grab and d-smash), and WD through you. The first two are countered mostly just by having decent timing and spacing on your aerial (jump immediately after your fair, or run away).
Beating WD through you requires a bit more finesse. If you've jumped, you are technically safe because the WD requires them to wait a period before they can action. Assuming you spot the WD, you can simply DJ > waveland off some platform and retreat or even possibly clip them as they pass with a bair or such. You can also predict the WD through and f-tilt. Fair > f-tilt is fairly reasonable pressure so long as they're over a certain percent and your f-tilt is spaced very, very well (tippy toes). ICs are weak at the edge because only one of them can grab it. If you can pressure them offstage, that's gravy.
When you launch ICs, make it a pain for them to come down. ICs have pretty meh priority coming down (dair sucks, fair is slow and hits in obvious places, bair is small, etc). Beating their moves when they are coming down is easy enough (trades are in your favour on almost everything). You should be wary of side-B; it jerks them horizontally when they do it (whether it's single or dual) so it's a pretty decent way of juking Sheik if she's too complacent. Although in all honesty the fact that they can't edgecancel it means they have to use the move's whole duration... which allows you to shark their landing with a whole bunch of nonsense.
Popo is pretty easy to tip up smashes on if he's recovering high with side-B for whatever reason. If it seems hard, just use a lot of bair & fair. Kill Nana whenever possible and abuse her AI to get efficient kills whenever possible (rather than d-throw fair, for instance, d-throw tipped up smash at a KO percent [requires you to keep a vague idea on how much damage she has]). Don't be afraid to jump off to kill Nana and recover onto platforms at low percents.
Nana's hitbox on Up+B stays out a lot longer than you think it does and she's probably invincible for most of the time in the air. So don't hit her when she's airborne. Just let her land and then kill her, or shark her husband instead.
Less solid ideas here and some questions of my own:
I find a lot of them have bad crouch habits and they like to swing with down smash. When you SH in for an additional aerial after you fair them (requires a hit-confirm but whatever) if you see they are d-smashing (and missing), it can be worthwhile to go for things that are not additional fair after certain percent ranges. I think dair might actually have some viability here after like 40% or so as a launcher to pop them up for a combo (that may very well kill them, and I'd really like to kill them more efficiently than I currently am).
Needles as a means to rack damage on them (full set of needles) on their next stock seems like it opens up a lot of options really quickly. I find as soon as you can start fishing for safe things to get them in the air then the MU is a lot less boring and much more manageable because it doesn't feel like you're fighting a wall that death combos you with pure poking.
Can you down smash them at the edge and hit them with the extra hits when you push them off? I'd be interested to know that.