Axe

Use Battle Hunger off cooldown on opponents' support usually.

It is good to fight the opponents while you are surrounded by enemy creeps to proc Counter Helix with more attacks. If needed, toggle creep aggro to force Counter Helix when fighting

If you can't pressure opponents' carry on the lane, consider creep skiping and farming neutrals in their jungle past 5 minute mark.

Encourage your supports to stack for you as you can clear stacks very quickly and early.

Don't roam around too much. Focus on getting Blink Dagger timely.

Use Battle Hunger on creeps to run around faster.

Once you acquire Blink Dagger, try to make use of it immediately and avoid showing yourself on the map too often. Comboing it with Blademail usually results in easy kills.

Grab illusion runes and make use of illusions to push out lanes as Counter Helix works on them as well.

When initiating, make sure you have allies that deal damage nearby.

Axe's Battle Hunger can be removed by getting a creep kill.

Avoid being close to Axe if you have bunch of allied or neutral creeps next to you.

Bring an extra hero to gank Axe if he starts creep-skipping.

Keep checking Axe's items. Be aware of his Blink Dagger and Blade Mail timing.

Don't clump up in teamfights or Axe will kill you all!

Consider buying an Eul's Scepter to use it on Axe quickly after he jumps your allies.

On Cores, Lifesteal and status resistance items are good against Axe's Call and Blade Mail combo.