Greater Mark of Attack Damage
Olaf's damage scales best with AD. Armor pen. is bad, because his main damage source is Reckless Swing, which deals True damage. Also, we don't buy attack speed because we don't need any jungle items, meaning that our clear speed relies on our Undertow damage, which scales 1.0 with AD. However, because the jungle items now give a decent amount of gold, I will probably be testing out Madred's Razors and Spirit of the Elder Lizard. I still think attack speed will be pointless, even if you take one of these, because Olaf gets enough already from Berserker Rage and Tough It Out.

Greater Mark of Critical Chance
We replace one AD mark with crit chance. This gives us 1% crit, which, if you get lucky, can make all the difference in getting a kill early game. We get the 1 AD back later, so don't worry about that.

Greater Seal of Armor
Always. The jungle camps hurt quite a lot, and without these you will need to buy too many wards or base too often. There are no good alternatives that we're missing out on, anyway. Unless Riot nerfs the jungle camps, which I doubt, these are ALWAYS necessary.

Greater Glyph of Magic Resist
This is where the choice comes in. I usually prefer flat MR, because early game I like to do a lot of invading, as well as forcing 1v1s and 2v2s, especially mid lane. By late game, I usually have Spirit Visage and Maw of Malmortius anyway. However, there are good alternatives:
* Greater Glyph of Scaling Magic Resist if they have weak early APs (e.g. an AD mid and Vlad top with an AD jungler) or you don't expect to be meeting any AP damage early game.
* Greater Glyph of Cooldown Reduction if they have no AP at all, or if you are confident enough without any MR glyphs. These will give you a fantastic damage boost early-game, because you don't start upgrading your E until later, so this combined with the 5% mastery will allow you to spam E on enemies like hell early-game.

Greater Quintessence of Attack Damage
Same reason as marks above. You will have good early game damage with flat AD marks and quints. Greater Quintessence of Movement Speed is an alternative, if you prefer to run between camps faster. However, we already have Ghost and CC immunity with Ragnarok up, so I feel that the raw damage from flat AD quints is far superior.

Ghost
This synergizes very well with Olaf. Once you buy some CDR, you can literally perma-slow someone with Undertow if you pick up the axe every time, therefore because Ghost lasts for so long, you can chase someone for eternity. It also synergizes with Ragnarok, allowing you to pop both at the same time and speed through the entire enemy front-line onto their ADC in no time at all. It's magical. Olaf is just one of those few champs that Flash sucks on. Alternatives:
* Exhaust if they are stacking a lot of hyper carry-type AD champs, like Vayne, Kog'Maw, Tristana, or even Jax. I would only take this if they have at least 2 of this kind of champ that needs to be shut down in late-game team fights, because in this case, just one Exhaust from your support might not be enough. Also, I might consider this if the enemy jungler is Aatrox, Jax or Lee Sin. This way, I can invade them at Lv2 and probably win the 1v1. However, it's risky to lose Ghost, so think carefully.
* Ignite if you really, really need it. I mean, if they have a team stacked with sustain. If at least 3 of the enemy champs rely on heavy sustain to survive, like Vlad, Mundo, Aatrox, etc. this is definitely viable. However, once again, think twice if it's really worth losing Ghost.

Smite
Speaks for itself. You need to smite to help your clear speed and, more importantly, to go for clutch buff, Dragon and even Baron steals at any point. They nerfed its early-game damage, but it still scales up to 1k at level 18. Its cooldown is lower too now, meaning that you can definitely use it on your first buff if you don't want to invade. I still usually go for smiteless, because I want to be certain that my Smite will be up for my Lv2 invade.

Berserker Rage
For every 1% of his health missing, Olaf's attack speed increases by 1%.

This means that if you're at 20% health, you will have +80% attack speed. This means that when you are at low health, you deal incredible damage with auto attacks and also because your Reckless Swing resets from auto attacks, and you become extremely hard to kill if you can get in melee range with Tough It Out. A great passive that synergizes perfectly with Maw of Malmortius.

Undertow
Olaf throws an axe to a target location, dealing 70 / 115 / 160 / 205 / 250 (+1.0 per bonus attack damage) physical damage to units it passes through and slowing them by 35 / 40 / 45 / 50 / 55 % for 1.5-2.5 seconds based on distance travelled.
If Olaf picks up the axe, the ability's cooldown is reduced by 4.5 seconds.
Cooldown: 8 seconds

Your signature spell. This is one of the main reasons you are viable. With a bit of CDR, you can literally keep someone slowed forever, as long as you have mana. However, it takes some time to get used to. Furthermore, this is your main jungle clear spell. You want to make sure it hits all the creeps in the camp to maximize your clear speed, and make sure you keep picking it up.

It's fairly easy to hit when chasing a target, but it can be a pain when ganking from behind: if you throw it too far behind the enemy, then you can end up creating too large of a gap between you and them when you pick it up and they run in the opposite direction.

Tough It Out
For 6 seconds, Olaf gains 9 / 12 / 15 / 18 / 21 % lifesteal and 40 / 50 / 60 / 70 / 80 % attack speed. He gains 1% extra healing for every 2.5% health he is missing.
Cooldown: 15 seconds

This is one of Olaf's less flashy or exciting spells. However, it's incredibly important. This is the ability that allows you to sustain so well in the jungle with no lifesteal items and very few potions, if any at all. Furthermore, when combined with your Berserker Rage, using this at low health will make you surprisingly hard to kill, and the enemy will usually underestimate your survivability when you are almost dead.

Reckless Swing
Olaf deals 70 / 115 / 160 / 205 / 250 (+ 40 % of total attack damage) true damage to his target. If he doesn't kill his target, he inflicts 30 % of the total damage dealt to himself as true damage.
Basic attack reduce the cooldown of this ability by 1 second.
Cooldown: 12/11/10/9/8 seconds

This is the spell that allows you to hit so hard without building a single AD items. With just a bit of CDR and a few auto attacks, you can chunk any enemy squishy incredibly fast, and even hit their tanks pretty hard, too, because it's True damage. It's also the only ability (other than ult) which reduces its CD per skill level, which is mostly why we level it second, as it gives us a huge damage boost per skill level. Nothing to say about this, really. It's incredibly easy to use. Just use it before you start auto attacking someone, then spam it whenever you can on your target and watch their health disappear.

Ragnarok
Passive: Olaf gains 10 / 20 / 30 armor and magic resist.

Active: Breaks any crowd control effects. Olaf loses the passive bonus armor and magic resist, but gains 40/60/80 bonus attack damage.
Cooldown: 120/100/80 seconds
Duration: 6 seconds

This is the main reason that you remain viable into mid-late game. With its passive, you gain extra tankiness for mid-late game duels and skirmishes, as well as jungle clearing of course. However, its active is the important part, as this allows you to completely ignore all CC for 6 seconds. Yes, you read that correctly. Ignore all CC. That means you LITERALLY CANNOT BE STOPPED. BY ANYTHING. Pop this along with Ghost at the right time, just as a team fight is breaking out and each team is throwing out CCs, and run straight through the enemy's front-line onto their squishy ADC or APC, then do free damage to them for 4-5 seconds. (Don't even worry if you die after that, because by this time you will probably have removed at least one squishy from the fight, as well as drawn a lot of cooldowns from your team onto yourself, allowing an overall victory and possibly an Ace.) It also gives you EIGHTY FRICKING AD (at Lv3). That's almost two B.F. swords for 6 seconds. The damage you will deal with this on is unreal. Be careful when using this, though, because for its duration you lose the free armor & MR, making you slightly squishier. However, because you have CC immunity, you can generally get free auto attacks off, allowing you to lifesteal with Tough It Out, minimizing this issue.