Parodied: Olaf wields a giant axe, with a spare on his back and a hatchet on his hip for emergencies - he also has throwing axes and a foldable pocket-axe. His banner is crossed axes, and his armor is made of axe-heads welded together.
Zig Zagged: Sometimes Olaf uses axes and other times swords. Occasionally he's even seen using a spear or firing a bow. But he's always prone to waxing lyrical on how amazing axes are, although sometimes he'll be caught in injuries he clearly would have avoided if he hadn't been using an axe at the time.
Enforced: "Olaf is badass. Badass characters need badass weapons. And what's more badass for a viking than an axe?"
"Wow Olaf, it almost looks like you have an axe fetish."
Olaf's battle cry is "TIMBER!"
Invoked: Olaf wants to cultivate a brutish, wild appearance, and decides he needs an axe in order to complete it.
Exploited: Olaf's enemies all use ranged weapons, taking advantage of his axe's short range.
Defied: Olaf hates fighting with axes, and avoids using them even when they're the only weapon readily available.
Discussed: "Okay the enemy are almost here. Everyone grab your weapo-NO OLAF NOT THE AXE THIS TIME"
Conversed: "So he's finally got his first fight scene! Why's he using an axe? Where did he even get that from?"
Deconstructed: Olaf charges into battle with an axe. He is quickly killed because an enemy pikeman skewers him from a distance before Olaf is in range to attack.
Olaf charges into battle with an axe, and his skills with the weapon allow him to overcome his enemies despite their weapons having a fundamental advantage.
Olaf charges into battle with an axe. Instead of getting skewered by an enemy pikeman, he simply lops off the pointy end, negating his foes advantage.
Olaf has a poleaxe, halberd, or other such axe-based polearm, and thus can get close enough to a pikeman to counter his thrusts, while still keeping enough distance to avoid being skewered. After a brief scuffle, Olaf disarms his enemy and moves in for the finishing blow.