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 found 2 software records in the database related to .vsdx to .odg file format conversion.
Multiplatform software - convert vsdx to odg on any platform
A vector graphics editor
Convert from vsdx file format
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.
Graphic and diagram software from LibreOffice suite