Tried some games last night running a 21-9-0 Olaf and going for a more damage oriented build when possible.

General

The biggest thing that is going to mess you up as Olaf is accidentally using Reckless Swing on an unintended target. When laning, you can alleviate this by practicing using the tilde key `/~ + E, which directs an ability to only target champions. However, I find the key placement a little awkward, so I may see about rebinding it to an alternative that is easier to reach.

In team fights where there are no minions are around you just have to be extra careful about which champion you target or just rely on the fact that it will come off of cooldown quickly if you are constantly autoattacking.

You'll see a trend in the match-ups which is basically that Olaf beats the hell out of most melee champions or can hold his own in the ones that are more difficult if you itemize for it. And he has trouble with match-ups that can poke him with impunity or have really high burst damage.

Tips

Tough It Out is useful for tanking minion waves to help set up a freeze or keep them from breaking on your tower where you will have to fight the tower for them.

It is also useful for getting enough attack speed to get one autoattack off on each of the range minions if you are trying to farm under turret. Finish the minions off with another auto after they take a tower shot. If you think you might miss any then Reckless Swing can be used to get the killing blow or you can use Undertow in a pinch.

Get to lane early and walk up to the enemy minion wave to draw aggro and then walk into the middle top lane bush. This will cause the enemy minion wave to form up in a diagonal allowing you to get the first 1-3 creeps which out much risk of harassment, which in turn can potentially insure that you get to level 2 first.

21-9-0 Match-ups

Riven - You beat her in lane as long as you play reasonbly smart. She can be more useful in team fights with an AoE execute via Blade of the Exile and the AoE stun from Valor.

Start Cloth Armor + 4 Health Potions and 1 Mana Potions. Build an early Warden's Mail and some health whether than be a Ruby Crystal into a Giant's Belt or a Crystalline Bracer. Keep your health above half.

Step 1 - smack her with a Reckless Swing when she goes in to CS

Step 2 - wait for some of her minions get low and hit them and her with Undertow to see how she reacts. If she is good, she will attempt to dodge/shield the damage from Undertow with Valor. If she does dodge/shield the damage, then don't throw more Undertows at her as you will just be wasting mana. If she doesn't dodge/shield, then use Undertow to harrass her each time some of her minions get low or the shield from Valor disipates.

Step 3 - if she uses abilties to farm, then give her a love tap with Reckless Swing.

Step 4 - at some point, she is going to try to all in you because Riven. Care if she has ignite, but if you've built some armor and health you should be fine as long as you don't take damage from every one of her abilities plus her empowered auto attacks.

Don't panic even if she gets her stun off on you. Simply activate Tough It Out and hit her with Reckless Swing every time it comes off cooldown. When she realizes she is losing she is going to try to back out. Don't let her. Pop Ragnarok, slow her with Undertow, and chase her into the ground.

Rinse and repeat.

Ekko - this match-up is hard at 21-9-0. I would recommend 9-21-0 and an early Spirit Visage and Mercury's Treads or Boots of Swiftness. Dodge his Q, Timewinder on the in-bound trip and outbound trip. Remember that it moves backwards really slowly at the start of the backswing so even if you are going to miss a creep, wait for it to pull back. If you see him bat something know that Parallel Convergence is going to appear somewhere in your vicinity soon and he is going to try something or he and their jungler are going to try something.

Tryndamere - You make Tryndamere cry. Start Cloth Armor + 4 Health Potions + 1 Mana Potion. Build into Ninja Tabi and The Brutalizer. Make Tryn cry more. Follow-up with Blade of the Ruined King. Tryn should be weeping from all the farm he is not getting. After that build tank. You've got enough damage to erase his health bar every time you see him. Sure he has 8 seconds to be annoying after that, but he won't have any items or kills so he will not be nearly as scary as he would otherwise be.

Ryze - if you take Ignite and play your cards right you can kill him yourself. You might even be able to do it without ignite, but it is a lot less likely. However, when he gets his ultimate, Desperate Power he can out push you so you may need Teleport to keep up in farm or have the opportunity to pick up a kill in another lanes. Build Mercury's Treads then follow up with Spirit Visage then possibly some damage. Blade of the Ruined King or Youmuu's Ghostblade will help you catch him if you really want to. Basically don't get snared by Rune Prison too often otherwise you'll take a lot of free damage, dodge Overload, and just stay away from him when he has his passive, Arcane Mastery stacked. Poke him with Undertow to get his health down and then call you jungle in for a gank.

Gangplank - annoying. No counter play to Parrrley he just shoots you when he feels like it and he can pop Remove Scurvy to cleanse the slow from Undertow. You can kill him but it is not easy as it seems like Cannon Barrage is on a 5 sec cooldown. Start Cloth Armor and 5 Health Potions. Pick up Ninja Tabi and follow this up with a Giant's Belt into Randuin's Omen. I'd like to say go for some damage, but he'll just crit you and then you won't be able to apply your damage. If I were to do this matchup again, I would probably go 9-21-0 and just farm up. Ignite can be helpful to reduce his healing if you can set up an opportunity to all in him.

Ran into another Olaf player and confirmed that Gangplank is a pain in the arse to be playing against as Olaf. This Olaf player was even running 9-21-0 and it didn't go well for him. This GP picked up Statikk Shiv and Trinity Force and it made him really hard to hit with Undertow.

Yasuo - does surprising damage even early game. He can block Undertow with Wind Wall and his passive, Way of the Wanderer, gives him a shield if he has enough Flow. On top of all that he out ranges you with Steel Tempest and he can juke around you or onto you with Sweeping Blade leaving you turning in circles. Wouldn't recommend Olaf against Yasuo.

Irelia - has a lot of annoying tools under her belt. You out damage her from levels 1-4. Once she gets 5-6th level and a Sheen your life gets harder. Start Crystalline Flask, two Health Potions and a Mana Potion and make her pay for every CS she gets, but do not neglect your own CS to do it because you need more items than she does to really do your job well because you don’t have a gap closer. After that build into a Warden's Mail to slow her attack speed and follow that up with a Giant's Belt to deal with the true damage she puts out via Hiten Style. If the laning phase is going to be extended then buy Mercury's Treads to decrease the duration of her stun/slow from Equilibrium Strike. After that you can start building some damage. Try not to fight her when she has Hiten Style active, though I find it hard tell when it is active. Basically just assume that any time either she or you goes for and extended trade she is going to have it active.

Shout out to WHOBICK who's Olaf guide I used as a template when building a more damage oriented berserker.