Make sure that Axe is really hard to kill to be able to tank and push without to have to worry about dying. This line-ups of item will be the best (trust me) and will suit Axe the greatest.
You can easily push towers and get the creep kills when tanking, just make sure to avoid those hitter heroes or you might die. (Seriously, no grudge and just personal reasons but I freaking hate Sven when his attack speed is high). But let me tell you, when all the heroes clashes, you will have the upperhand. Trust me. Just activate your 1st skill and everything will be fine. As long as your teammates supports you. It will be a great game. Trust me.
You can even use Axe to carry and enter the enemy's base without ease and just troll. (When your regen is high and you are hard to kill of course.)
Blink and Blade Combo
If this is your first time using axe and might be a noob, (no offense) I'll tell you the trick.
First, if you are chasing after an enemy, blink first near the enemy then activate the Berserker's call (1st skill) and while taunted, use the blade mail, you can even cast your Battle Hunger (2nd skill) for additional stats and BAM! sure kill. If the enemy got a chance to run away, before he could even, use Culling Blade,(Your Special Skill dumbass!!).
This combo will be convenient when using Axe so remember this when choosing axe as your hero. Make sure that you first buy Blink Dagger before purchasing the Blade mail. Having possession of the Blink dagger will be enough when using the Berserker's call.