Not Updated For Current Season
Olaf is OP. For your skills, Ult is priority number one, Reckless swing is number two, followed by vicious strikes, and lastly your axe.
At the beginning of a fight, use vicious strikes before your first swing and then immediately use reckless swing. its important to know that when you use your axe, try to make the distance perfect so you can hit them but still retrieve it for the shorter cooldown. Since Olaf relies on items, try to get the last him, reckless swing and your axe work well for this.
For your first item, get boots of swiftness. Follow that with a Phantom Dancer(starting with either Brawlers Gloves or Cloak of Agility, which ever you have enough money for when you need to recall. Get another phantdom dancer and by at this point in the match you should be having some team fights. If someone in your team has Stark's Fervor, go for a Bloodthirster starting with vampiric scepter, other wise go for a starks fervor.