the idea is that i want to share documents over git
i thought about using Text Document (looks like docx,odt in functionality ) that can be edited with any text editor (
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: