Undertow is a versatile ability and offers many different utilities to Olaf:
It is a very useful ability for chasing because of its own cooldown reduction (if you can pick it up while chasing). Throwing your axe where you are likely to chase your opponent lets you refresh its cooldown much quicker and increases its slow uptime.
It is an effective harassment ability. While many skillshots are consumed upon hitting the first target, or will lose effectiveness as they do,Undertow will travel straight through all enemies it hits for full damage. At early levels, however, recklessly spamming it will swiftly leave Olaf without mana.
It will remove the fog of war in a large area around where it is thrown for a very brief duration, making it useful for checking bushes.
Although Champion sustained damage output isn't very powerful during early game, his burst is surprisingly strong as his Reckless Swing deals a significant amount of true damage which cannot be mitigated by any means. With a few ranks invested in the ability it can devastate the health of most squishier champions during mid-game.
If you have not invested in significant HP or health sustain as you level it, it can also fairly quickly devastate the health of Olaf himself if you are not careful with its usage. With this in mind, it can often be unwise to abuse this during a duel, as Olaf may potentially wind up helping to kill himself.
In lane Reckless Swing has a higher range than Olaf's basic attack range, this allows you to poke with it.
Ragnarok provides complete immunity to all forms of CC, and largely defines Champion playstyle during the later stages of the game. It can be used either to initiate a battle, to improve his fighting ability midway through one, or to make an emergency retreat if the situation starts to become disadvantageous.
Champion most common and effective role during late-game teamfights is to function as a bulky assassin. Upon the commencing of a pitched teamfight, Olaf can activate Ragnarok and dive straight through the frontline of the enemy team, singling out the opposing AD carry. Because of the complete CC immunity that Ragnarok affords him, he becomes extremely difficult for the opposing team to peel away. Even if Olaf is unsuccessful in slaying his target, the threat he poses is often enough to drive them completely out of the teamfight in their attempts to avoid him, drastically reducing the enemy's team's damage output.
Olaf is also a very useful peeler himself, operating to safeguard his own carry from the opposing team. His ability to chain-slow enemies with Undertow and the excellent damage output from Reckless Swing can make it extremely difficult for enemy champions to safely attack the carry without risking being kited and killed.
Olaf naturally receives armor and magic resistance from the passive effect of Ragnarok. Because of this, it takes more skills and time to kill him with the bonus armor and magic resistance, therefore stacking health on him is a very common build path.
When Olaf does not have Ragnarok or Undertow available for use, he can be extremely vulnerable to kiting. A Randuin's Omen greatly reduces the effectiveness of this tactic and also offers a considerable amount of health and a useful active CC which Olaf greatly appreciates.
Atma's Impaler is a particularly useful on Olaf - because of his natural tendency to obtain a significant amount of health, the bonus attack damage provided by its passive effect can be quite substantial. It also provides armor, improving his survivability, and critical strike chance, offering a powerful, if unreliable, boost to his DPS.
Spirit Visage is one of the best items that Olaf can purchase. It synergizes with Vicious Strikes, increasing the sustain that is already increased by the ability itself even more, not to mention any lifesteal item that Olaf is likely to purchase. The cooldown reduction is also a great asset to Olaf. Due to these reasons, this item is nearly essential for Olaf, except when there are no AP champions on the enemy team.
Olaf does not need Banshee's Veil that much because Ragnarok makes him immune to nearly every crowd control he would want to block with this item. However, it should still be considered if there is an important damaging spell that Olaf should block.
It is important to note that Blade of the Ruined King deals damage based on the enemy's current health. Generally, enemies want to stack health to mitigate the effects from the true damage dealt by Reckless Swing, but since BotRK counters this, there are very few things in terms of defense that enemies can do to mitigate Olaf's damage with this item. However, if offers lower raw AD, therefore less damage with both Undertow and Reckless Swing itself. The extra attack speed and the active from Ragnarok should compensate for that, however.
Also, Blade of the Ruined King does not offer minion clearing capabilities that Ravenous Hydra offers, forcing players to either buy Sunfire Cape or constantly spam Undertow to clear minion waves.
Heavy cooldown reduction also greatly benefits his Reckless Swing - with access to at least 284 true damage nuke on a 4.8 second cooldown at level 9, Olaf has excellent damage output from it alone, allowing him to dedicate the rest of his build towards improving his defenses and tanking ability.
Olaf has no dash ability, so augmenting his mobility with an early boots upgrade often proves to be very effective.
Boots of Swiftness are a good option in this regard. They make Olaf hard to kite, but at same time, they make him rely on Ragnarok to get rid of crowd control effects that are not slows. If those CCs are a problem, Mercury's Treads may prove to be a better choice.
It is important to note that Spirit of the Ancient Golem no longer offers tenacity, so Olaf should still choose between the two above boots when going jungle.
Olaf does not need armor penetration. When choosing between flat damage and armor penetration, it is better to go for flat attack damage because his main target is the AD carry with low armor and the true damage from Reckless Swing deals decent damage to tanks. Undertow also benefits from flat damage. If the enemy team is especially heavily armored, The Black Cleaver is still a reasonable purchase though as Undertow spam and basic attacks can quickly shred the entire enemy team's armor.
If your team plans on killing Olaf you have to fully commit in doing so; leaving the job-half done will make him even more dangerous due to Berserker Rage and he is likely to simply life steal all the effort your team put on him
Undertow is a slow projectile, meaning that you can dodge the spell easily.
You can deny Olaf from spamming Undertow by preventing him from picking up the axe that the spell left in the path.
In a similar vein, making significant course changes while Olaf is chasing you will prevent him from picking up his axe and continuing to close the distance on you.
Save your CC while Olaf is using Ragnarok. It removes and negates any CC cast on him while it is active.
RagnarokOlaf also gives him bonus armor and magic resistance. However, when activated, the passive bonus is lost and he gains a lot of AD to boost his damage. It might be wiser to try and burst him before the buff duration is over.
As Olaf is immune to any forms of CC placed upon him, the most effective forms of keeping him away are self-displacement abilities such as Arcane Shift and player-created terrain such as Cataclysm. You should try to save these abilities for when he uses his ultimate to make him waste the duration.