I always go for a simple but effective combo that can be adjusted to switch her out with a launcher, or keep her in if I don´t want to switch.
j.mk, cr.hp xx Tiger Strike charge
May sound weird but thats the start of the combo. You´ll have to confirm hit or block up to this moment and decide on your next action accordingly.
On hit [launcher version, 0 meter, midscreen]: j.mk, cr.hp xx CADCPC, cr.lk>cr.hp>launch — Deals ~330 meterless with Jin in the back.
On hit [no launch, 0 meter, midscreen]: j.mk, cr.hp xx CADCPC, cr.lk xx Tiger strike — OK damage, but I rarely use this one. If I want to keep her in, I´ll go for the 1 meter version nearly all the time.
On hit [no launch, 1 meter, midscreen]: j.mk, cr.hp xx CADCPC, cr.lk>cr.mk>cr.hp xx EXCADCPC, f.mk>f.mp>mp xx Wind Roll, cr.lp, b.mp>mp, cr.lk xx Tiger Strike — Not to shabby damage for a meter, corner carry like crazy and definitely stylish 
On hit [no launch, 1 meter, corner]: j.mk, cr.hp xx CADCPC, cr.lk>cr.mk>cr.hp xx EXCADCPC, f.mk>f.mp>mp xx Wind Roll, cr.lp, b.mp>mp, lk, f.hp, cr.hp xx Tiger Strike — Just like midscreen, just a different ender after b.mp>mp.
On hit [launcher version, 1 meter, anywhere]: j.mk, cr.hp xx CADCPC, cr.lk>cr.mk>cr.hp xx EXCADCPC, f.mk>f.mp>mp xx Wind Roll, cr.lp, cr.hp xx CADCPC, cr.lk>cr.mk>cr.hp>launch
On Block 1: j.mk, cr.hp xx Tiger Strike charge backdash — If they´re reversal heavy and start to get annoyed by your endless frame trapping, do this one and they´ll shoot into the sky, ready to be comboed by you.
On Block 2: j.mk, cr.hp xx CADCPC, cr.lk — Frame traps heavily and can be extended after the cr.lk [chain into cr.hp, then EXCADCPC or backdash. You can do whatever you want after that]
Woah, long post 
Now you know the exact play style of my Julia, change it to suit yours. As you can see, I´m relying heavily on CADCPC, but my setups keep her strong mixups quite safe and always result in a guessing game for the opponent. You need to find out if your opponent is reversal heavy or not, when you know what to expect from them the above combos should cover nearly every situation of you offense.
Hope this helped.