Disclaimer: I'm not an expert.
Don't know much about Olaf, but here's what I would suggest as Irelia. First, you want to max E for the stun. Second, you don't want to engage unless you have a clear advantage (like a jungle gank, not just a few more HP than him). Farm, punish engages with your stun, and focus on sustaining and winning lategame.
If you're looking for straight-up counterpicks, go with someone who can either duel him evenly, out-sustain him, or poke/kite him. For the first one, you have other juggernauts - Garen, etc. For the second, you have champions with a lot of built-in sustain - think Cho'gath and Maokai. For the third option, you'll mostly be looking at ranged champions, but be aware that some players will be able to counter this strategy, depending on the champion you use.