Latest versions of LibreOffice can open and import MS Visio drawings (.vsd, .vsdx etc.) just fine and you can use the LibreOffice Draw program to re-save the diagram to OpenDocument ODG format. You can download the suit for free, so this seems to be the easiest and most convenient way.
Convert Microsoft Visio drawing to OpenDocument drawing.
We have found 3 software records in our database eligible for .vsdx to .odg file format conversion.
Multiplatform software - convert vsdx to odg on any platform
Apache OpenOffice Draw (OpenOffice.org Draw) is a fully-featured graphic editor that allows users to draw quick sketches or complex diagrams. It is easy to use and has many nice features. Draw comes as part of OpenOffice.org productivity suite.
Convert from vsdx file
to odg file
The tables with software actions are a good pointer for what a certain program does with various file types and often may give users a good hint how to perform certain file conversion, for example the above-mentioned vsdx to odg. However, it is not perfect and sometimes can show results which are not really usable because of how certain programs work with files and the possible conversion is thus actually not possible at all.
LibreOffice Draw is a useful software tool for creating various drawings, diagrams and other simple graphics. It's an open source program that comes as an integral part of LibreOffice suite.
Inkscape is vector graphics editor that using with W3C standard Scalable Vector Graphics (SVG) file format. Inkscape supports many advanced SVG features (markers, clones, alpha blending, etc.)