Here's my feedback. Uh, I apologize for the wall of text. Just how I do. :)
Passive: Nanite Infestation
stacking infinitely per target.
Nanites are removed once a champion dies, or if Vascillion dies.
Infinite stacks is a risky proposition, I think, especially since there's no maximum duration beyond either champ's death. One misplay can spell certain doom, and not in the fun, time-Sivir's-Spell-Shield-to-block-Karthus-ult kind of way.
Allied champions passively get Nanite stacks while standing near Vascillion.
The way this is written, it's technically a bad thing, but I understand your intention. You want nearby allied champs to also benefit from Nanite stacks. Seeing how the ult works, might I recommend changing the name of the ally stacks so that it's clearly a separate effect? Consider Nano-Boost, as opposed to Nanite (enemy) stacks.
Do allied champs also benefit from (infinitely stacking) attack speed? Someone like Guinsoo!Kayle would be utterly horrifying.
Are these allied Nano-Boost stacks also potentially infinite?
Q: Nanite Recall
dealing damage per stack.
See, again, infinite stacks means /infinite/ stacks. That means potentially infinite damage, which is a big no-no. It becomes very, like, "Either I approach Vasc and try to shut him down but risk losing a massive chunk of health from the get-go, or I spend the whole match running away from him and he's totally shut down my lane." That's not fun to play against.
Does this ability deal damage PLUS damage per stack, or do you need to apply stacks to deal any damage? I think actually the latter might make for interesting gameplay, but you'd need to let stacks decay over time so Vasc can't nuke from 100% health after a drawn-out battle.
W: Nanite Bomb
Medium cooldown, meant to help with jungle clear and CC in lane/ganking.
Active: Nanites inside of all nearby enemy units explode, dealing physical damage per stack.
So, Q rips the nanites out and W detonates them. From both a gameplay and a flavor perspective, these don't feel different at all. The way it's written, it sounds like they both remove all stacks from the target(s). That might be fine--if you want that, make these abilities feel REALLY different. You could have one ability spend all stacks to deal damage with a small splash effect and the other spend all stacks to deal less damage with a movement speed buff--that creates an interesting dynamic, I think, where the enemy has to think about what you're likelier to do.
Passive: All units in range with Nanite stacks are slowed by 10% per stack of Nanite infestation.
Yikes. Taking it literally, you'd need only ten stacks to completely immobilize someone. You wouldn't even have to engage them; just being in their presence totally shuts them down.
Additionally, gain movement speed towards any slowed champions, increased by the total number of Nanite stacks pulled.
I'm assuming this is only towards champs Vasc himself slows? What if he's got a Rylai's?
When allied champions are near Vascillion, he grants them movement speed towards him with each stack of Nanite Infestation.
This, I like. It's /towards/ Vasc, so it's a useful get-in/get-out type buff, but that's hardly game-changing.
E: Nanite Wall
No complaints here. Seems like a solid enough defensive ability.
R: Luster Purge
Passive: Allied champions recieve stacks twice as often and recieve one stack each time Vascillion uses any other ability. (This passive only works while the ability is off cooldown and available for use.
This effect has potential. I'm just beating a dead horse about the active effect, but to reiterate: Infinity is a bad sign. There are times where it works, like with Veigar's passive: he's MEANT to be a total glass cannon, and it fits thematically with his whole megalomaniac-supervillain-delusions-of-grandeur deal. Here, though, if Vasc can effectively give his teammates infinite bonus attack speed, teamfights are gonna be really skewed in his team's favor. I'm not saying he would definitely win--Randuin's exists--but then you're forcing itemization, and I don't think that's a good road to go down.
General feedback
How about "the Technopath" for a title?
I'm not really sure how nanites in THEIR body make YOU faster, but I guess that's League for you. We've seen weirder.
These names are pretty similar-sounding. I recommend changing them to make them feel more flavorful, memorable, and distinctive.
Could you edit these to list what stats Vasc should be building and what his damage types are? I see his W and R do physical damage--do they scale with AD? Is that the case for his Q as well? Maybe he builds hybrid?
I'm mentally pronouncing this name "VASS-ill-on"--is that accurate? Vass-ILL-ee-on?.......dude, it kinda looks like "vasectomy".
What about this for an overall concept: Vascillion is a bruiser-mage hybrid who depends on his abilities to get him in and out of fights and close the distance. Within melee range, he's a force to be reckoned with, especially as time goes on, but he doesn't have very many options from afar.
That way, it's clear how to counter him--keep your distance, try to kite him and slow him down. He has clear strengths and weaknesses.
Alas, this doesn't address the elephant in the room: Vascillion doesn't feel really notable. I believe--and I think Riot would agree--that a new champ should introduce a new angle of gameplay. Kayn's forms make him adept at countering both melee and ranged teams. Ornn opens up new items for his team and doesn't have to retreat to arm himself. Zoe steals Summoner Spells, and both she and Ornn introduced new CC effects. Kai'Sa's items seriously amp up her abilities to an unprecedented degree. Vascillion....builds infinite buffs for himself. It's just not the same. It doesn't have the same kick to it at all, to be honest.
I really do think you have the makings of a good idea here, but there's still a ways to go.
