As of right now, there are like 420 build paths 
can go. Right now my current build path is
- Bottom 3 aren't in any order
- Built during the late laning phase
My runes are typical Azir runes with 15 percent CDR @18 Masteries are 21-0-9 Going Down Wanderer Path Ending at Runic Affinity No points in Meditation
I think you should ditch the CDR runes, get some AP runes, build morellos for mana, and wreck some ass
I've played a few Azir games now, so you could say I know a thing or two :^)
The important part is the runes, cdr scaling blues, ap quints, hp/level OR armor yellows, mpen reds. Cdr blues allow you to hit that 40% cdr with only one cdr item because Azir is not Fizz and he does not build lucidity boots.
RoA is an item you generally want to stay away from. If you want early tankiness grab 2 or 3 dorans rings. Later on you don't really need tankiness because you have zhonya to prevent dives and enough range to avoid a lot of damage from most champions. Build morello first instead because you get a lot more damage and the pieces of morello are both useful on their own. Catalyst doesn't do much for you and codex is just better than blasting wand because you get cdr. If you really want hp then rylai is a better choice, but it doesn't really have any synergy with Azir since it doesn't allow you to get more autos off of your Qs and it doesn't really help with landing your kiting because Azir uses positioning to avoid damage instead of kiting.
Nashor's tooth has long since been replaced by cdr blues + luden's. With the RoA build you would usually be building this second, but morello first you can go straight into luden's for way more damage.
After Morello + Luden you can finish off your boots. Always get t2 boots before void staff, and usually before your third item.
After you've got your core morello, luden's, boots, zhonya is an option if you're getting dove, death cap is good if you want more damage, void is good if the champions you're hitting have a lot of magic resist.
If you're looking at pro builds, you'll see the build abyssal a lot. Abyssal is solid if you're consistently fighting your opposing midlaner or if they're a big threat in fights/skirmishes. Think Ahri, LeBlanc, and Ekko. Build it immediately after morello or not at all.
tl;dr: Morello -> Luden's -> Sorc Shoes -> Dcap -> Void -> Zhonya
