Neutrinos passing through black hole
No, you have a wrong understanding of the Wikipedia statement. Wikipedia says only "Gravity is extremely weak" on a subatomic scale. It does not say "neutrinos are not affected by gravity".
They cannot pass through a black hole just as light cannot pass through a black hole. Photons are even lighter (no mass is as light as can be!) than neutrinos, and photons are certainly at "subatomic scales" (they are fundamental particles!) and so if photons cannot escape black holes, neutrinos can't either. (In fact nothing can - that's why they are black holes.)
neutrinos are not affected by gravity on the subatomic scale
Where do you get this idea? It's not a part of mainstream physics.
One of the main ideas behind general relativity is that gravity isn't just another force battling it out in the arena of physics; it is the arena. That is, gravity is really just the geometry of spacetime, and anything (including a neutrino field) in spacetime is experiencing that geometry.
So no, standard physics does not predict that neutrinos will be able to escape a black hole. Instead, standard physics predicts that everything that enters a black hole's horizon will be unable to exit the horizon, including neutrinos. No one has done an experiment that can test this theory because we don't have very good neutrino telescopes or very good access to black holes. And it's possible that standard physics is wrong. But that's all we can say for now.
EDIT: In the comments below, the OP points out the underlying confusion that led to this question, which is the role of gravitons in black-hole physics. First of all, gravitons are (as @probably_someone points out) not really a part of mainstream physics. In particular, we don't know how to formulate a complete working theory of gravity using quantum field theory. We can quantize linearized gravity, which is the basic reason anyone really bothers to talk about gravitons, but that doesn't extend to nonlinear gravitational systems. And that's the key point: black holes are very nonlinear (unless you're very far away).
One consequence of this is that you can't model a black hole as a particle that interacts with other particles via exchange of gravitons. That's just not how our current theory of physics works. There's a related question with a very nice answer here, where Jerry Schirmer points out that the graviton is an excitation of the gravitational field, and not the field itself — but it's the field that makes a black hole, not its excitations. You might want to appeal to quantum field theory in curved spacetime, but even then, you basically assume a background curvature to spacetime. And it's that background curvature that affects the motion of the neutrino and traps it inside the horizon.
The black hole will gobble up the neutrinos for lunch and think "Mmm, what a yummy little snack!" :)
Seriously. Neutrinos are just tiny bits of massive matter, and thus they will be consumed by the hole in the same fashion that any other matter will be. The non-interactivity of neutrinos is that they are not interactive with the electromagnetic and strong force, which removes most of the interaction with ordinary matter because these two forces are very strong, and thus comprise the bulk of what makes ordinary matter highly interactive, while the other two forces, which neutrinos do interact with - that is, the weak force and gravity, are much weaker. Thus the first two forces account for the vast majority of the interactivity of ordinary matter and so particles ignoring them will have greatly reduced interactivity. But in extreme conditions, these "weak" interactions can become much stronger, and the black hole is an example of an extreme condition.