Since anisakis worms are not readily recognizable in the flesh of fish without a powerful light, or in the case of red-colored fish, a UV-light, they are not nikkar. Even so, they are a complete non-kosher entity where a part of it is considered a part of the whole, and so the whole anisakis worm is considered a berya. In terms of bliyot, they are mius, and are certainly batel given the amount of surrounding fish. But in terms of the worm itself, it is not batel because it is a berya, and even in 1000 X it is not batel. This din of berya is discussed in Yoreh Deah siman 100.
However, as the Taz discusses, and as Aruch Hashulchan brings down as pashut, this idea that it is not nullified even in one thousand times the amount (rather than mere taste or 60X) is a din derabanan. And there are implications. To cite him inside:
The idea of the importance of items such that they are not nullified is a Rabbinic law. For since, Biblically, there is this importance such that we lash on its consumption even when it is less than an olive's measure, for it is plainly (setama) written regarding impure species that you should not eat them, even if they are small, therefore the Rabbis were stringent regarding mixtures of them. However, Biblically, they are nullified just as other prohibited items. And the practical distinction here is in terms of a case of doubt if it is a berya or not, it is a case of Rabbinic doubt, and it is nullified. And so too all the things about which we say in future text that they are not nullified, such as rauy lehitkabed or davar shebiminyan. However, if it is certainly a berya, or one of these which are not nullified, but rather the prohibition is a doubt, in this even in 1000 they are not nullified. Such as eggs of something which might have been a treifah, and the like. And so writes the Issur beHetter, Klal 25, law 7.
If so, an opportunity to be mattir these has opened and then swiftly shut. We might have said that berya is a din deRabbanan, and so in any case of safeik, it is a safeik deRabbanan and it is lekulah. But while Taz indeed indicates that it is a din deRabbanan, he says that they did not establish it like that. Rather, if there is doubt whether the berya is present in the first place, then it is a safeik whether the Rabbinic law of berya not batel goes into effect, and so safeik deRabbanan lekulah. But once the entity exists as a complete entity, even if there is a doubt as to its prohibited state, Chazal would indeed apply this rule that it is not batel since it is an entity, and the origin safek deOrayta stands. Thus, it would be assur.
What about by anisakis? There are two sefeikos we can posit. The first is whether it is in the fish, or in any given piece of fish. This would be the first type of safek mentioned by the Taz, whether the berya is present. I suppose that the osrim could or do counter that in wild salmon and the like, it is so prevalent that there is no safeik. I am not certain about this -- in any slice of fish before me, I would guess that there is indeed a safeik.
The second safeik we can posit regarding anisakis is whether they are assur in the first place. Everyone now agrees that the worms in the flesh come from the belly. The worms in the belly are assur misafek, because maybe they came from the outside, or maybe they hatched from eggs inside the fish. This is the understanding of Beis Yosef and Pri Megadim regarding the worm in the belly. Rav Belsky asserts that worms in the flesh must have come from eggs that hatched in the belly, such that worms in flesh are vadai muttar -- and that was what Chazal meant. The osrim must hold that they have the same status as worms in the belly, and so are assur misafek. If so, perhaps this is safek berya and is nullified? It would seem that we cannot say this, for the safek deOraysa applies to the issur, but there is no safeik whether they are berya! Thus, Taz ruled this out.
I will try a more novel approach to make this not berya. There are different ways of understanding berya, that of Rosh and that of Ran. Both are brought lehalacha in Shulchan Aruch. According to Ran, it is not a berya unless the issur applied mitchilat beriyato, from the moment of its creation. So, for example, a non-kosher bird is a berya, but a kosher bird which became a neveilah is not. These tolaim, these anisakis worms, are assur misafek in the belly. Why are they assur? Because maybe they were shoretz al pnei hamayim, or maybe they were internally generated.
Assuming that Chazal and Rishonim understood them to be spontaneously generated, then they initially were regular sheratzim which had not yet been shoretz, but subsequently they moved from one fish to the next and were indeed shoretz. Thus, in their initial state they were muttar and only later were they assur. How can they be berya?!
Assuming that we are operating via external vs. internal generation / hatching, then I would guess that they are saying in this case that maybe the anisakis eggs hatched inside the water (rather than the other fish species), and were swallowed as larvae. If so, they were shoretz in the water. And presumably they were shoretz in this manner rather immediately, once they emerged from the egg. Perhaps we can make the argument that for the one instant, they were not. Or we can say that that some are shoretz later reveals this aspect to be an extrinsic rather than intrinsic factor. It is a sheretz, yes. But there is a sheretz which has not yet been shoretz and a sheretz which has already been shoretz. As such, maybe we can argue that it is not a berya! (Certainly, we should be able to say it is not a berya for something that was initially entirely muttar for a while, and only later escaped and was shoretz on the water.)
The major problem with this is that while it works well with the theory of the Ran as I understand it, it seems to be against an explicit Mishna. In Makkot 13a, which we learned a few days ago in daf yomi, the Mishna discusses berya, in terms of being liable for eating a small amount, less than a kezayis. (This is the explicit statement regarding berya, whereas that it is not nullified even in 1000 I think comes implicitly from the relevant sugya.) And the example is אוכל נמלה, eating an ant, which Rashi explains is assur because of sheretz hashoretz al haaretz. Maybe they operated under a correct presumption that all ants are shoretz on the aretz from birth, as opposed to the anisakis worm, where it depends on the stage of development and pace of development? Perhaps, even so, this chiddush is somewhat difficult to say.
Also, even if we do say it is not berya and therefore would be batel, this is presumably only if it is not nikkar. I think it is not nikkar if we need a very bright light to spot them, or a UV light in the case of red-colored fish. But maybe the osrim would disagree with that assessment.
I should note that even if we say it is berya, there is still a reason to be lenient. From a purely Biblical perspective, it was batel. Only Rabbinically is it not. And the same Rabbis who said that it was not also said that these particular worms in the flesh are muttar. (I made a similar argument in the past regarding the safek whether they were present and the safek whether they crawled, under a disputable view that safek deOraysa lechumra is a din deRabbanan. But here this seems to clearly be a din deRabbanan.) So I am solid in terms of Chazal. And even if I am not, so I am violating a din deRabbanan when there are major Rabbonim such as Rav Belsky who give straightforward reasons to be mattir besides this; and where all generations, from Moshe Rabbenu to Rav Moshe all ate this fish and believed it to be muttar. And I am countering an unfortunate trend to go looking for reasons to prohibit everything by selectively applying scientific discoveries and wish that the Torah was given to malachei hashareit. I am OK with possibly violating a deRabbanan given all these (and other) factors.
Note: Not intended halacha lemaaseh. Consult your local Orthodox rabbi.