What are the best ways to organize one's research workflow when using multiple Operating Systems? I have a good memory, but some of the fields I'm working in (NLP, Semantic Web, Information Visualization, Machine Learning) are quickly expanding. 

While I do have a good method of keeping track of good research (I only follow the best researchers and research groups on Twitter, Scholar, conferences, journals, etc), sometimes perhaps it's better to save all the interesting papers, add notes to them and put them in context and relationships with other papers (if a paper frequently cites another paper and is a sequel to that paper, perhaps it's better to read those 2 papers together, for example). 
Essentially the things I want to do are these:


keep records of the workshops, classes or tutorials I attended, but also
video recordings of presentations I have never seen in real life
annotate PDFs, extract metadata from them and generate bibtex
bibliographies
keep tutorials in pdf + video format synced (where possible)   
keep everything in context - organized in folders, tagged,
cross-referenced if possible (if an article is cited in a paper and I
already have it in my library, I want to be able to access it fast)
I want to be able to search about various keywords/tags regardless of the location where the actual files are stored and OS.


I noticed most of these things are doable in the Apple ecosystem (iTunes, iBooks, etc), but not really on Windows and Linux. Does anyone has any idea about how to do this in Linux and Windows? I happen to absolutely need to use both operating systems (still have some work with SQL Server, Excel, etc), but most of my development work is in Linux (coding in Java, Python, JavaScript and others, but also writing papers in LaTeX).

I would preferably only sync a huge zotero (or similar) folder using Dropbox, and papers/tutorials should be in sub-folders named after their research field, but also tagged so that I can find them regardless of the folder. 

EDIT: 
I have paid Dropbox, but apparently finding free WebDAV is an issue (therefore that would mean an additional 5-10 euros per month). As far as code goes I use GitHub and GitLab. 

After seeing your answers, it occured to me that I'm thinking about it too much. Perhaps the best idea is this: the whole workflow should be a webapp - this way it will perform almost similarly on all operating systems, as even if there are differences between browsers, they are not so big as the differences between OSes.
Here's what I do, to manage everything between a Mac laptop and a Linux desktop. I usually write code and do heavy lifting on the Linux machine, but when at home or reading / writing documents I use OS X. 


All files of a manageable size are synchronized with BitTorrent Sync. You could also use Dropbox, but that costs money for >2 GB. BTSync is free, unlimited, cross-platform, and peer-to-peer.
If I'm writing code or TeX using TextMate on my Mac, but executing it on Linux, I just run rmate on a document on my Linux machine and the file pops up in TextMate on my Mac. It's wizardry, I tell you. It beats waiting 5-10 seconds for cloud synchronization to catch up.
I use Papers3 for my paper library, which synchronizes with my iPad. All the PDFs are kept in my small, free Dropbox account - the file organization is a bit obtuse so Papers3 is in practice Mac/iOS only. Papers3 does have a Windows app, but not Linux. Mendeley will sync with its Linux and Windows apps, so that might be your best multi-platform option for document storage and annotation.
I have not used Evernote recently, but it runs using Wine in Linux. That's another option for syncing notes and documents.


I'm not aware of a tool for Linux which comes anywhere close to Spotlight for Mac. If there is a program that will synchronize file tags and such across operating systems, I'd like to know about it! Otherwise, for advanced "metadata" and such you're usually restricted to the ecosystem of a particular application.