The idea is that I want to share and track documents over git
I thought about using Text Documents (markdown docs that look like docx,odt in functionality) that can be edited with any text editor (not binary). Where to find something like this?
any better solution?
Have you considered using LaTeX instead of doc or odt? This way you can edit the documents with any text editor and get good looking results. Better yet: you have proper diffs between revisions (no matter the SCM you use).
If you don't like the idea of editing the document in a simple text editor take a look at LyX. It provides a gui for editing documents like you would get in normal document editors.
For git hosting solutions you can use: