I don't play aatrox, but as a Jax main here's some advice to beat him:
-Fight him when he doesn't have your minions to dash through (or when it would be a bad idea for him to do so, dashing under your turret for example)
-Break his passive shield with your W or an AA when possible (if he gets close enough to you to last hit that you can W/AA him)
-After 6 you can easily beat him with 2 AA on a minion + Q + W, repeat until he gets low enough to all in
-As Jax your E will NOT dodge his Q damage, don't get baited into this
-Try to save your E for when you're sure you can hit him with it, or to activate before his ultimate hits you
-If he misses his tornado he'll need to Q something twice to get it back up, so punish him during this time
-Try to move unpredictably when last hitting minions, so he cant land free Qs on you
-Max your E next after W, save Q for last
-Consider taking
or
to help you win the lane
**For build advice (since you asked specifically for that):
**
-Early
is fine, good choice vs yasuo
-
first if you're winning lane,
first if you're behind
-You can beat him after you finish
(assuming he's not an item up on you or anything)
-You can grab
or
for the slow active and sustain to easily duel him
-You shouldn't need to, but if you're REALLY having a hard time vs him try going
as well as
, this will neuter his damage (as well as enemy adc)
If you do several (or all) of these things, you shouldn't have any problem beating silver Yasuos on Jax
Good luck!