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I partially agree with Peter K.’s answer: contacting the editor is one way to proceed, although admittedly it’s a somewhat drastic step, and you might want to consider more gentle approaches first. A respectable journal will be very cautious about publishing work with controversial authorship, so at the very least this could buy you some time to try to resolve the situation. It’s possible that the journal will also actively help to establish the facts and mediate the dispute, although I’m less certain about that part.

With that being said, I think before you start throwing around accusations of “illegal”, or even just unethical or inappropriate, behavior, you need to think carefully about the logical basis for your argument. From your description of the situation I’m actually not sure you have a strong case, although your collaborators’ behavior may reasonably be seen as nasty or uncollegial. What I’m understanding, roughly, is that the project has two parts, one (let’s call it “part A”) that was the work of the collaborators, and another, let’s call it “part B”, which was your work. The plan was originally to publish both parts together, but now the collaborators decided that they only want to publish part A. Well, I’m afraid you can’t force someone to associate their name to a work they don’t want to be associated with, so although you are understandably upset about the removal of part B, personally I think the collaborators are within their rights to remove it and tell you you’ll have to publish it on your own if you want to see it published. The real question, and the one I’d advise you to focus your argument on, is your authorship on the new version of the paper that only contains part A. If they put you in an inferior place on the author list relative to where you feel you deserve to be, that’s something you should discuss with them.

Anyway, good luck.

Edit: on further rereading of your question I am slightly confused about the precise events here. Are you still a coauthor or the shorter paper? Are you still one of the first authors? Are you complaining about anything other than the removal of part B? Did the collaborators get your approval to submit the shorter paper with your name as a coauthor? If they didn’t, that would be a legitimate thing to complain about, but if the shorter paper was indeed accepted to Nature, I would tend to agree with Wolfgang Bangerth that they might have actually done you a big favor - the longer paper might well have ended up not being accepted, and now you get a publication in Nature and an opportunity to publish another, separate paper as sole author.

I am adding a short answer based on your updated question, now containing all key points.

I agree with you in that it must be infuriating to see 5-years-worth of your time flushed down by your colleagues behind your back. I have worked in such a group setting, in a highly competitive institution. I had colleagues in similar situations. Years of dedication and long meetings, lab work, learning, dedication, and the feeling that you don't relate with the final outcome.

If you want to fight this battle, I believe others have provided you all relevant advice here. I just want to tell you what I'd do.

Your feelings are justified, but: (i) this is how ambitious institutions work, most of the time, and you cannot change that; (ii) working in a production line is frustrating as compared to the artisan's life, however it is favored by modern society (read Karl Marx on this); (iii) as others say, you'll end up with a nice publication on your CV and apparently the freedom to reorganize your data for another subsequent publication; (iv) modern academia is mostly about prestigious authorships and not quite about morals/personal values/human development; (v) any serious players involved will crush anyone standing between them and some "Nature" paper.

You are worried about justifying your contract time based on your publication outcome. Well, if you fight this war you'll finish your contract with no paper, and the accusation of being a troublemaker. Also I believe you're exaggerating this issue: likely you'll have enough justification as long as you don't mess things up (which you're considering doing right now). I therefore suggest you accept their conditions, finish your contract, take some time off, and then come back to your own work and objectives.

Drink this poison, digest it later. Good luck.

During my PhD I was also part as a computational person in a developmental biology project that made it into Nature. In contrast to your case we always discussed and agreed on how to proceed. Since the experimental results were spectacular, my contribution was kept at a bare minimum and buried in the SI not to upset any referees. Actually, the whole presentation was geared towards that: not upsetting any referees. Even after acceptance the text had to be reduced by a substantial amount. In my opinion the final paper does not really do justice to the whole project, so I can vividly imagine how you must feel and what is going on.

However, I don't think it is worth risking a CNS paper (particularly as first author) over presentation (if e.g. your statistical analysis would be interpreted in a misleading way things would be different). Furthermore, I don't think it is worth worsening the relationship with your colleagues. Publishing in Nature is a dirty business, but it certainly helps your career and it might help you publishing your work in more detail elsewhere. After all having a follow-up paper is almost as important as having the CNS if you are looking for a job. And not having letters of recommendation from involved big wigs would be a huge red flag.

I would strongly advice you to talk to a senior person you trust and who knows as much of the story as possible. I have never heard of legal steps helping anyone in academia. If you think it helps, I am happy to share my experience over Skype or something.

It is my understanding that articles in Nature have an almost "pop science" appeal, even though they have a very high impact factor.

Prudence thus dictates removing highly technical portions of the manuscript, and publishing them elsewhere. I know that after I read a paper in Nature, I know that I need to find the follow-up details either in the supplemental material, or in another journal.

I worked on a project much less impactful than this, but where a similar situation took place. After working on the project for a year, we were ready to submit the whole group paper. Then the group leader contacted my supervisor and wanted to cut out the part that included our work because of space constraints. Ultimately we substantially reduced the portion that described our part of the work and the group paper was accepted in a relatively high impact journal. So I took the rest of the material I had worked on with my supervisor and put it into another paper, for which we have just gotten back a revise and resubmit.

I recommend the same path to you. Take your material and make a standalone journal paper. All of a sudden, instead of one publication for your years of work, you have two. Perhaps your contribution can go into a journal important for your specific field. While you may be correct that the Nature publication may not seem quite as cool since your field's contribution is minimized, transdisciplinary research is important, and a Nature article is a big achievement. At my institution, which is a major research institution, such publications get highlighted in the internal news and bring other kudos as well to the authors.

The politics in a big group effort can be intense, and you are too junior to burn all your bridges on this one. The time for making the point you wanted to make was sooner, and the heavies in the group didn't agree with you. As your career continues this type of politics will continue to exist. Unless there is truly an ethical concern, it is probably not worthwhile to fight the tide on these. Also, keep in mind that we can all be a little blinded to the big picture. Think of all the musicians who have left groups to pursue their solo careers and then disappeared from view. Perhaps the article you have cowritten has been pared down to be a true classic for the related field.

In general, publicaltion requires permission or a license, but the license may be implied and may not always be revocable.

You marked this as a legal issue. As always, my only advice is that you speak with a competent lawyer in your jurisdiction if you have any thoughts on taking legal action. The legal issue will be copyright, though false light claims or right of publicity claims could also come into play depending on the full circumstances.

Generally, in the USA, an author including a joint author, gains copyright over their work and may use that copyright to block publication of the work without their permission even if the co-authors wish to publish. (Exceptions such as fair use, legal privilege, and de minimis use exist, but these are far beyond the scope of the question)

With that said, remember that permission once given cannot always be immediately withdrawn in the context of copyright. If, hypothetically, a joint author were to give permission, even implicitly, to publish at the outset of a project they may not be able to withdraw that at the end even if they are dissatisfied with the work in its finished form. I refuse to give legal advice on this forum so I will not ask about your specific situation, but as a general rule most academic collaborations I have dealt with have involved giving that permission towards the beginning. Large scale ventures involving grants and financing often have this explicitly in a contract or collaboration agreement. Smaller scale lower-cost ventures often have more informal arrangements but still involve conduct that would grant an implied license to publish that may be hard to withdraw.

Note that this particular question may truly have different answers in different jurisdictions since Moral Rights (droits moraux) vary significantly between countries.

A word on ethics

The ethics of the situation are another matter. While reasonable people may disagree, I personally feel it would be unethical or at least unseemly for your co-authors to publish this with your name and your work before they reach some sort of compromise you feel to be acceptable, which in this case may be splitting the matter into two papers which are submitted to journals in different fields.

Chances are that your university or institute has a policy to follow the Vancouver Protocol, or similar. This would give you good argument to confront your director, and to escalate to a higher hierarchy in your institute if he is not willing to discuss the matter. Like this, you take justified action without escalating too much. It is totally possible that the whole thing is merely a misunderstanding.

There is no rule how much contribution is required to be listed as an author. So, while you feel that "the key findings are also the fruit of [your] work", the other authors may feel that your contribution was not enough to be listed as a co-author. In that case, they should list you in the acknowledgements, at the very least.

Edit: I am referring to the ICMJE Recommendation "Defining the Role of Authors and Contributors", particularly the first criterion

Substantial contributions to the conception or design of the work; or the acquisition, analysis, or interpretation of data for the work

and the clarification

All individuals who meet the first criterion should have the opportunity to participate in the review, drafting, and final approval of the manuscript.