Having played Vlad for the whole day here are my insights.
Laning
Vlad is still extremely good at laning safely. I have not fed a single lane today playing Vlad (it's team fights where the wrong calls can cost you). During laning phase, E should not be fired except OCCASIONALLY in Snapshot mode to last hit. It should just be Qs and auto attacks non-stop (this is the best way to stay Sustained as well as to damage the enemy economically)... FORGET that you have E. Only use it to last hit VERY occasionally. Just auto and Q. If the enemy goes All-In no you during laning, just step back and fire Q. Using this strategy, you can survive laning very well.
I start boots and then try to land my empowered Qs on the enemy laner. If you can't (because its heavily telegraphed and he'll soon learn to just step back when you turn red), its not the end of the world. Just fire the empowered Q on a minion for the extra healing and damage and farm.
Only use charged E IF you get a jungle Gank AND you are sure you can land it. Otherwise I repeat... it's just Qs and autos to farm and harass non stop.
Using this strategy, more often than not, you won't die in the lane and will farm quite well (unless you are camped and constantly over-extend, but that's also why E is not fired except very rarely).
Use W only to escape the direst of attacks and only at the last minute.
This strategy works against Mages AND assassins. The only difference is that if its an assassin, rush Zhonya components first for the amor (instead of going Abyssal first or Hextech Belt first).
Teamfights
Basically, the New Vlad can also deal ''snapshot damage'' like the Old Vlad but it has been Nerfed. You play like you are the Old Vlad except you acknowledge that you have less damage when kiting. If you're poking, just hit them with Qs and SNAPSHOT Es. Don't bother charging E when you are poking, its too telegraphed, they will just move back and you will hurt yourself. Just snapshot fire it and only as a second resort when Q is not available.
There are basically 2 scenarios in terms of Team Fights.
- Poke Phase
This is where people are exchanging fire at each other with neither side committing. Perhaps both sides are assembling their laners; no one has initiated anything yet or committed their forces.
At this stage Old Vlad was a lot stronger (because his fully stacked Es generally ALWYAS hit and had no real health cost because of Spell Vamp) and Old Vlad's Q was always at full power.
You can't do anything about this. Just play like the Old Vlad, fire snapshot Es and Q the enemy. Don't worry about charging your Es in Poke Phase (its too telegraphed, you'll just hurt yourself), don't bother with checking your Q meter just pretend it doesn't exist. If you HAPPEN to have the Hextech Belt up and your Crimson Rush procs at the right time (situational), then sure... hit the Belt, hit the empowered Q and then back off as a poking manoeuvre (where it's safe).
The advantage of firing Snapshot Es is that there is no health cost (yes you deal almost no damage) but it can help with Poke DPS when Q is off cool down.
Just resign yourself to less damage here than Old Vlad but make better decisions in 2.
- Decisive Battle
This is where after some Poking (or without), one side commits their forces and goes all in. They may or may not have Initiated properly, it may or may not be a good play.
Decide if you want to go in or not. If you do, start using the fully/half-charged Es as the main damage source but spam Q as well. ONCE the enemy has committed, they are less able to counterplay your telegraphed Es. Try to time and aim your Ult well. This is where THEORETICALLY you can out damage Old Vlad.
Don't go TOO ham, make sure you retreat as soon as you see your side starting to lose. But if you aimed your Es and Qs well, hopefully at least one enemy will die.
As soon as a decisive battle is over, go back to Poke Phase mode (snapshot Es and Qs).
Using the above general strategy and building full AP, I managed to get dramatically better and even acceptable results in terms of damage.
The theory behind is very simple. Assuming your Laning Phase doesn't go extremely long (now it COULD since Vlad wants a farm lane and sometimes it turns into one while the war is decided in the other lanes) and assuming the war comes to the Mid Lane (I play Mid Vlad)... following the strategies is optimal for damage output.
It makes sense that you should max the number of times you are hitting the enemy in Poke Phase. Its not a decisive battle and so people are VERY aware of you and whether or not you are trying to charge an E or whether your Crimson Rush is coming. Just maximise the number of times you hit Qs and snapshot Es, its the best thing to do here.
But ONCE you get into team fights where one side has committed... THEN it makes sense to start hitting them with charged Es. Because they've committed, they are less able to counterplay you (and in many situations, counter playing your E means getting hit by other attacks from others). You'll notice that in this Decisive Battle phase, your Es and your third Qs will start to hit (again, I don't advise basing your plays around 3rd Qs but to just take advantage of it intuitively if it procs because its way too hard to plan/predict 7 to 5 seconds ahead).
If you do the above while prioritising survival, your damage should go way up...
doesn't use 
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