Where ODD came from
OpenDocument Drawing is the ISO-standardised drawing format used by LibreOffice Draw and OpenOffice, part of the ODF family adopted in 2006. It holds vector shapes, text boxes and embedded images in a zipped XML package, and turns up in public-sector and European workflows where ODF is mandated by policy.
The technical picture
Compression: Zipped XML. Transparency: Supported. Animation: Not supported. Colour: Vector and embedded raster. Typical file size relative to WebP: varies with content.
Where it opens
LibreOffice and OpenOffice. This is usually the deciding factor when choosing between ODD and WebP — WebP renders in every browser but is uneven in desktop software, while ODD has a very different support profile.
Converting ODD to WebP
Rendering an ODD drawing to WebP produces an image anything can display, without needing LibreOffice installed. Vector shapes are rasterised and can no longer be edited as objects.
Converting WebP to ODD
Wraps your image in an OpenDocument drawing so it opens directly in LibreOffice Draw for annotation and layout. Expect the ODD output to be varies with content — that difference is the price of getting a format the destination will actually accept.