As most things, it really does come down to preference. The way I understand it though is you want to go Dorans + Pot with these runes(You can opt for Taste of Blood as opposed to Sudden Impact) in easier match-ups or when you are confident in your skill vs the opponent. Corrupting with these runes when it's a harder matchup or you just want more sustain.
The stat shards come down to preference, some people like going double adaptive instead of AS + adaptive to make Q resetting on minions early easier as well as giving you a little more early game damage for your all-ins.
Even higher tier Irelia players still opt for Inspiration second and I personally really like the sustain it gives so I use it in most matchups, plus Timewarp has saved my ass plenty of times already.
As for items, again it comes down to preference and how you want to play the game. The one core aspect in every build is BotRK. She has options for her mythics, I go TF most games but opt for Sunderer in games against a lot of tanks. Gore drinker is an option as well and some people are finding success going for a tankier build and grabbing Sunfire. If you plan on team fighting Sterak's is a must, but you could probably opt for something else if you want to split push since it won't be as beneficial.
Experiment a bit and see what fits your playstyle better and what feels better to you. Also in a range matchup you could probably go Resolve second and grab Bone Plating to help out, although I don't find myself really doing that ever but I know it's an option.
As always anyone can feel free to correct me or add onto what I've said, other than that I hope this helps!