Illaoi, Fiora, and Irelia are all very good at split pushing. Now, I don't play top lane much, but I do somehow have Fiora at mastery level 6, so I know the role somewhat, and I've been playing since season 1 and really just have a lot of game knowledge.
Farming vs a Ranged Champion: You'll typically need to use your ranged spells to farm vs a ranged champion, either to poke them out of lane or to kill the minions. The other way is to just stand very far away from them, since they will outdamage you from range, and let the wave push in on you. This way, you can farm under the safety of your turret.
's Q is good waveclear, poke, and it heals you if it hits an enemy champion, same with the W if you have tentacles nearby to slam them. Once you have all 3 spells, use your E on them to pull the soul either into your turret or just into some tentacles and whale on it. This will force them to either back off or all-in you, and either way you win that trade.
's Q always prioritizes champion vitals if it can, then anything it will kill if it hits, then the nearest enemy if none fit that criteria. Use it to last hit under turret or to initiate an all-in on an enemy champion, and remember that you can use W while dashing with Q (I do this all the time when I try to fight a Veigar, I dash into the wall and pop W before I hit it to absorb the stun).
's Q resets if it kills the target and refunds some of the mana cost. It also applies on-hit effects (things like Sheen). If the enemy champion is standing next to a nearly dead minion, Q to the minion, then immediately stun them, activate your W, and start hitting them. This way, you also get the reset from the minion, so if, say, a Quinn E's you to get away, you can jump after her with your Q and continue the chase. You can also just use Q to last hit under turret.
Starting Items: For all 3 of these, I would think to go Doran's Blade or Corrupting Potion, depending on the matchup. I think Gbay99, a diamond-level YouTuber who mains Irelia, always starts Corrupting Potion on her. If you know it's a rough matchup, start Potion. If you know you can beat them, start Blade.
Where to stand in teamfights:
As I said, all 3 are great split pushers, meaning that you can just choose to go top lane and split permanently if you want and nobody should be able to kill you solo. This is an especially good tactic if you are behind or not the only person with a tanky build (with Illaoi and Irelia), making you less needed in teamfights. Basically, these guys are all melee and need to get in there to have teamfight impact, so if you don't think you can get into a teamfight long enough to actually deal damage, just pick a lane and push until either someone comes to stop you or you have towers that are easier to take on the map. For splitting, bot lane is the most important inhibitor in the game to get because that puts pressure on the bottom lane, which is the furthest lane from Baron. Getting a bottom inhibitor could very easily mean that they have to send multiple people bot to defend it if they let the wave build up enough, which can easily give your team a free Baron. However, you typically want to go either top lane or bottom lane for your split, depending on where your team wants to apply pressure elsewhere on the map. If they want to try to go for dragon or a bot lane tower, go top lane so that anybody who comes to stop you is guaranteed to not make it to a teamfight in time. If it's a baron or top lane tower your team is trying to get, go bot lane for the same reason.
As for teamfights, Fiora and Illaoi are very good in teamfights, but I'm not sure about Irelia as much. Fiora and Irelia I would expect to play like divers, basically assassins, but tankier. They try to dive onto the enemy ADC and force the ADC to focus them. Fiora can burst them down pretty quickly, using her ultimate to give her a heal field when she does and her W to block some damage/cc. Irelia can't burst them as fast, but can draw their focus for a lot longer. However, make sure you can get onto and stick onto the enemy ADC with both of them. If you can't, especially for Fiora because of the ultimate and vitals, it's better to just hit the tank if you can't safely get onto the enemy ADC and kill them.
Illaoi, on the other hand, plays as a damage tank. You get as close to the middle of the enemy team as possible, rip someone's soul out with your E (because that counts as an enemy player for your ult), then immediately ult. The tentacles will start bringing the pain on the enemy team as you spam your W, using your Q whenever you can. If you can't safely get into the teamfight, it might just be better to use your Q and E to poke from range, letting your tentacles and your team kill any souls you get with the E.
Fiora:
Matchups:
Fiora is very heavily countered by anyone who can cc her for extended periods of time while dealing damage. Illaoi can also be annoying, since no matter what, you can't use your W to block her E, however you can use your Q to dodge it. She's very strong vs tanks with lower amounts of cc because she can proc her vitals on them for a lot of damage. Any time you are looking for a trade, try to get your vital to spawn on a side that's easy to hit, dash in, then use your E. If you think they'll cc you during your dash, use your W to block it. Garen is a pretty annoying matchup in the early game. Pre-6, use your W on his Q to stop the silence, then start hitting him with your other spells, hitting vitals whenever possible. Once he has ult, always save your W for it. It deals too much damage for you to not have the W absorb. Riven is entirely a skill matchup. If you let her bait out your W, you'll lose to her. If you don't, you can use the W to stop one of her cc spells pretty easily and stun her. Get a sense of how that particular Riven plays, and adjust when you use W accordingly. If they use the Q on you 3 times, then W, use the W when she's using the third Q. If they use the Q twice, then W, use the W after the second Q.
Build:
I typically like to rush Tiamat, then get the Black Cleaver, then finish Hydra, but it's really up to you. Spirit Visage is almost always a must-have because of the heal increase; it'll make your ult field and your vitals heal you more, which is always good. Death's Dance can also be a pretty good item. Youmuu's, GA, and several other items can also be good. For Runes, go attack speed reds, armor yellows, magic resist blues, and AD quints, or alternatively, AD reds and attack speed quints. Getting 10% CDR in blues might also not be a bad idea, but I personally find that I typically build 40%, so the 10% is unnecessary for me.
Masteries:
Ferocity: Fury, Fresh Blood, Vampirism OR Natural Talent, up to you, Double Edged Sword OR Battle Trance, up to you, untested but I think Battle Trance would be better, Battering Blows, Fervor of Battle
Resolve: Recovery (not going to be building enough Armor/MR for Unyielding to be useful), Tough Skin or Siegemaster, depending on matchup and if you want to let them push towards your turret, Runic Armor because better heals from passive + ult, and then the tier 4 is really your choice, but I personally like Insight.
Illaoi:
Matchups: I think that any matchup has the potential to be good or bad for you, depending on how you and your opponents play it. Hitting E's on your opponent is some very oppressive poke, meanwhile you also have strong pushing with the tentacles.
Build: either
or
, depending on if you need to be a wall of fat for your team or not,
first item if you aren't going for
that game,
can be good,
,
,
,
can also all be super good.
Runes: I think AD reds, armor yellows, MR blues, and health or % health quints can all be good, but I'm not too sure. I typically just run my fat tank page of exactly that.
Masteries: you can run either a damage heavy or a tank heavy page. For damage, 18/0/12, doing pretty much the same thing as Fiora, but I think a tankier page of Fury, Feast, either Talent or Vampirism, Battle Trance, pick one, pick one, Runic Armor, pick one, Swiftness, and Grasp are best.
Irelia: I don't play this champion, I have no clue. For items, I know the extent of Trinity Force into full tank, maybe Sterak's, and I think she runs Fervor for masteries. Other than that, I'm completely clueless. Sorry I can't help this one as much, but I don't even own Irelia.