Short answer: Jax's counterstrike dodges everything that's considered an auto-attack.
There are a lot of fuzzy lines around what exactly auto-attacks are though:
Physical damage is not synonymous with auto-attacks.
Those are 2 separate things in LoL that simply share a strong correlation.
You can have magical auto-attacks (Teemo) and physical abilities (Riven).
You can also have magical abilities that are considered magical auto-attacks (Warwick).
Towers play by their own rules, taking damage and dishing it out in a very exotic way compared to everything else.
The important thing to note with them concerning counter-strike is simply their Penetrating Bullets item states their auto-attacks ignore dodge. So, while tower attacks are technically auto-attacks: Counterstrike doesn't do anything against them.
Jax will generally evade on-hit effects from attacks he evades.
Kinda worth noting because Fiora and Pantheon will not, and Pantheon can actually block turret shots with his AA exclusive defensive measure.
Not sure about the specifics here. On-hit effects have their own incredibly weird rules: but it seems Jax will evade them if they piggyback off of an auto-attack. If it's something like Cho'Gath's Vorpal Spines that's essentially an ability cast every time he AA's, Jax won't dodge that.
Any ability that applies on-hit effects is counted as an auto-attack.
These are also treated as auto-attacks for the likes of Ninja Tabi, Thornmail, Warden's Mail, Randuin's Omen, Doran's Shield, and any Auto-attack based masteries as well.
Such abilities can apply things like Tiamat, Hydra, Lizard Buff, Frozen Mallet, Sheen, Trinity Force, Lich Bane, Iceborne Gauntlet, Entropy, Essence Reaver, Kingblade, and life steal.
It's also worth noting such abilities do not apply the ability-hit effects of Rylie's, Liandry's, Luden's, or spell vampirisim.
Also: Critical strikes, for whatever reason, are considered a very separate thing from on-hit effects.
You may notice Gangplank's Parrrely ability specifically states it can critically strike AND apply on-hit effects, listing critical strikes as a separate thing.
Additionally: Black Cleaver and Muramana simply apply to "physical damage", playing by their own rules and not the basic on-hit rules.
So Judgement, Alpha Strike, and Spear Shot will strike through counterstrike, being treated as abilities and not auto-attacks, applying Muramana and Cleaver effects right through counterstrike.
However: Blade Waltz, Infinite Durress, Siphoning Strike, 3-Talon Strike, Tumble, Decisive Strike, Double-Up, Parrrley, Mystic Shot, Twin-Bite, and a respectable number of additional skills that apply on-hit effects will be treated as an auto-attack for the purposes of Counterstrike.
Anyways:
Jax's counterstrike blocks auto-attacks.
What counts as an auto-attack or ability can general be seen via a simple test:
Anything that applies life-steal is an auto-attack.
Anything that applies spell-vamp is not.
