Tips to Use Axe (Dota2)

• Axe is especially dangerous early game with high starting statistics and the speed from Battle Hunger contributing to his ability to push up to the enemy tower relatively safely, even for a semi-carry.

• Berserker's Call provides the full armor bonus at level one. It is the primary factor in his ability to survive physical damage without good statistics.

• Resist using Culling Blade when not roaming. While Axe is powerful early game, he levels stat-wise fairly badly, and it is best to drop kills to a carry past the point when a team acquires their ultimate.

• Items such as the Vanguard, Hood of Defiance and the Shiva's Guard are essential as they help reduce the damage being dealt to Axe while he tanks and initiates a battle without a Blink Dagger. With a Blink Dagger, this aspect can be ignored when initiating to an extent.

• During the early phase of the game, a Stout Shield is all Axe needs to survive the lane. If possible, instead of fighting along with allied creeps, Axe can try to go and clash with the enemy creeps by himself with Counter Helix allowing him to take down unstacked creeps by himself.

• A more advanced technique used by players is to max out Battle Hunger by Level 7. This enables Axe to constantly deal dots (damage over time) in the lane, dealing crippling damage and blocking any potential to push or counterpush. This meshes well with Axe's capability to tank and keep the enemy at bay while stopping them from last hitting or denying creeps, allowing Battle Hunger deal its full damage.

• If Axe is going against two weak melee heroes in a lane without sufficient burst damage (such as Phantom Assassin or Spirit Breaker, etc.), do not hesitate to stand between them and their creeps. It allows for complete lane dominance as they cannot last hit and it denies them of experience and gold as Counter Helix hurts a lot early game.

• You can put "dota_health_per_vertical_marker 300" in the console without quotes to easily find the instakill hp thresholds for Axe's ultimate. Change the number according to Axe's ultimate. This sets each bar of health to the value you set, which means when they are under 1 bar of health, you can ultimate. This can also be applied to Dagon, but Magic Resist should be factored in.

• Axe is an excellent counter-pick to heroes with abilities that can greatly increase their attack speed (i.e. Ursa, Troll Warlord), as a combination of Berserker's Call and Blade Mail can be devastating to such heroes, especially if Counter Helix procs numerous times.

• Instead of using Berserker's Call to draw creep aggro in lane, it's usually better to right click enemy hero (which automatically pulls the creep aggro). It applies to any enemy heroes visible on map, thus you can pull aggro by standing in the middle of wave and right clicking visible enemy on the other side of the map. 

source: http://dota2.gamepedia.com/Axe