Countering Axe?

Well, sure - but if he's left the lane instead of creeping cutting and/or harassing your carry, I'd put that down as a win. You can your support buddy can go stack/roam/gank while your carry gets freefarm and solo XP. Certainly, it's very hard to shut Axe down completely, but being able to smack him down that hard at level 1 means he has zero lane presence.

not if you have bad laning supports or are in a low MMR pub where lanes are chaos and often have a 2 1 2 setup, you look at it way too black and white. and its not like the axe cant get help himself.

so for support counters either ones with heavy harass, skywrath, AA, lina with her range, visage, veno, dazzle, or ones that make him take more damage. level one wave on venge, shadow demon.

I Have actually played some potato tier 0K MMR pubs with friends who were starting with dota not that long ago. Whenever there was a creep-skipping Axe, the solution was essentially limited to calling your mid player for an early lvl 3-4 gank. Like "hey Lina do you want two free kills top?". Always works.

Axe creep-skipping essentially boxes himself in. There's only one escape path for him and it's exactly the path that a mid hero would gank him from.

I mean seriously the only problems I ever had with creep-skipping Axes in the past year or so were when he was in my team. When the guy goes back to creep skipping even after feeding 3 kills...reported :)

Yeah but an Axe whose jungling from the off is missing one of his timing windows. And it means your laning core can get free farm, and you don't have supports who are forced to keep the Axe in check, thus they can be more greedy with there actions and rotate more easily.

So in essence, forcing the Axe to jungle is a win, especially if you can force him there before he gets his Tranqs.

All you need to do then is be wary for the reveal of the Blink Dagger, which is usually a kill, and after that play as you would do against any Blink iniator, because his damage out-put has long since peaked.