That's basically it. I'm fully aware that it doesn't address every single problem, but it will do the job in most casual and ranked games. These are rules of thumb; nothing more, nothing less. I do make a few points here and there (like avoiding the rageblades, getting some armor shaving stuff, etc.), but it's all subject to circumstance. I have neither the time, the patience, nor the skill to come up with a response to every single situation you could be faced with as Jax.

Ok, then it works great. At higher elo they always run away so make a notification about maxing Q or W if they just run when you dodge or maybe don't change anything at all as those at higher elo won't use a guide (actually I came here to help people with guides) but I think it will grant you better votes.

The problem is, everyone keep attacking when you activate dodge. It might be that they don't see it, or are just slow; but I have yet to see anyone run away the moment I activate dodge (unless they're being ganked or are poking).

Good that you added black clever. I would recomend maxing W first then Q and last E. At max lvl W got a base cd on 3 sec, it reset autoattack timer cuasing you to attack twice in the almost the same time as on autoattack (if you time it good).
Also the mana cost of E increases by 5 with each upgrade (goes from 70-90 mana cost). Your build don't include much mana early and you are required to use E for trading if you max it. You will go OOM to fast and have much weaker duel potenesial. Also If you opponent don't auto attack you during dodge(which they should not be doing if the faced a jax before) it will deal very little damage.
Overall it won't be too strong. Uppgrading W gives more damage, lesser manacosts and much strong duel potential.
Maxing E so the cooldown decreases (assuming that it allow you to use it twice) is strong later on when you have two slows, in your build after trinity force.
Before that people will just run away as soon as you activate dodge and then you won't hit enagh many AA for it to be more damage than if you maxed W.

I've actually been experimenting with several variations of this build. Some success has been seen in replacing Nashor's with a black cleaver. Boots, on the other hand, are highly situational from what I'm seeing.

EDIT: An amazing amount of success has been seen. CC reducing boots and the Black Cleaver make all the difference when you're being ganked by Garen, Mundo, and Katarina all at once.

It's not enough, you will still go down really fast in teamfights. If you get stunned and focused for 2 secs you would go down against most teams (if you didn't activated E in time or if they focused you after it expired) if they too have finished their builds.
Just change nashor's thooth as you will only get 6% less cd-reduction.
Boots give 15% cdr, masteries 4% cdr and elexir 15% providing a total of 34% just 6% from the cap.
Also the attackspeed from nashor's tooth cuases you to exceed the as cap on 2.5
Base AS 0,8+0,8*(trinity force 0,3+nashor's tooth 0,5+elexir 0,42+jax passive 0,86+runes and masteries 0,45)= 2,82.
Now if we remove nashor's tooth we goes down to 2,42. Just 0,08 attacks each second from the cap.
So the nashor's tooth will provide 0,08 Attack per second, 6% cooldown reduction and 65 ap (which Jax don't scale that good with). The mana regen won't matter lategame when you have a big manapool.
I may have got jax base AS wrong so you may not exceed the AS cap with that much but still.
There are other items that will benefit you far more.
You should aim for an hp item. I don't know which good hp items there is on the new 3v3.
I will come back later with a item suggestion.
Try which AS you get without nashor's tooth but with elexirs. I may have counted wrong somewhere.

That complaint of yours holds water until level 6. At that point Jax's ult provides the necessary armor and MR. It's somewhat sporadic, yes. But you really don't need it long considering your damage output, lifesteal, and spellvamp. To add to this, consider the fact that you carry several debuffs on you at all times.

You have way to little tankiness, I know that it's hard to get on TT but you really need it. With this build you will melt down to the oppenent's burst without having time to deal any more damage than your burst which won't be much.
Jax exells at dealing sustained damage meaning that you will have great profit from staying alive long.
I would suggest switching nashor's tooth for something tanky.
Also consider to start boots dorans as the lifesteal won't give much before you got more ad.
Another route I like is actually: boots, mana crystal and 2 health pots offering you the same sustain as a vampyric scepter will and also allow you to switch clarity for something more useful as heal.
It will take about 45 auto attacks to get healed for 2 pots (300hp) with a vampyric scepter (at low lvl with 60-70 in ad) and the pots also regen you the health much faster allowing you to zone out your opponent (or avoid getting zoned yourself).
An early shen combined with bilgwater cutlass will ensure you epic harass and epic sustain.
I will revisit later.