Is it possible to publish without adviser? I participated in an exchange programme as a PhD student for 1 year in another country. The very moment I got in the new institution I signed a contract according to which I have no intellectual nor material rights over the results obtained on the territory of the lab I joined.
The subject of my study has changed on the go so after the first 4 months I started different analysis compared to the one written in my project (project funded by academic exchange program).
After going back to my home country my local adviser asked me for the results I have. I refused to submit because I am not the owner and because I found out my adviser is sharing my work with another student for money. Almost 3 years later and after repeating some of the results in my home country I managed to defend successfully.
However I would like to publish my research from my exchange programme. The issue is this:

My foreign adviser is not responding quick enough to my messages - it took him 4 years to revise part of the paper. And I am planning on writing another two!!!
My foreign  adviser retired.
Apparently my both advisers made some sort of a deal to hand over my work to the student I described above.

What is your advise in that situation?
The response to this depends to a degree on the type of institution you were studying at and the norms for that educational system.
In most countries now the norm would be for the Graduate School to have the final say on matters like this. Particularly if the advisor(s) involved are retired (or remaining as semi-retired adjuncts).
Given your OS research was on exchange, the Graduate School at the host institution would typically defer to that in the home country on matters like this.
If the agreement you signed appears to be binding they may discourage you from publishing. If not, I expect they would encourage you to publish. They may even recommend this irrespective of the opinion or the status of the advisor, but that would depend on the culture (and politics) of your home institution.
Graduate Schools often have expertise on these kinds of issues as IP issues are common in collaborative projects. Broadly speaking, most Graduate Schools want their PhD candidates and graduates to be publishing. It's a good look for them and its what they are there to support you to do.
My advice would also to be raise the apparent sharing of your work as a separate issue. Not that I'm saying don't raise it - but if your goal is to be able to publish the results of your research then aim to sort that out as a separate issue.
I would then consider if you think that the sharing of findings with other students looks like the kind of academic misconduct that is defined by your institution and if so consider raising this as a separate matter. I would handle the prospect of academic misconduct with care if you are thinking of raising this.