Text editors

Hi Visvanath,
It is technically feasible to support ODT, but quite a big job, so it's unlikely to happen any time soon.
However, LibreOffice 4/5 can save ODT files to Word 2010 .docx format, which should import reasonably well.
As far as I can tell, OpenOffice doesn't offer the same facility to save to Word 2010 format, so you're out of luck there.

I only recently started using LibreOffice, and I haven't done much testing of how well the plugin imports .docx files saved from LibreOffice, but I believe that headings, embedded images, character-level formatting and tables should all import OK. I think numbered and bulleted lists won't import very well, as the import depends on style names like "List Bullet" and "List Number" (the built-in Word styles) to work properly. LibreOffice doesn't have these named styles, so lists will import as plain paragraphs, I think.