ODA Drawing Explorer uses Drawing SDK and allows to change the DWG database. ODA Viewer uses Visualize SDK and doesn't allow any changes in database (but certainly allow to change some visualize settings like visualize styles, parameters of the lights etc). Drawing Explorer focused on the DWG database while ODA Viewer is about the visualization.
You can find the source code of the ODA Viewer application in the following archive (only for ODA Members):
After unpacking the archive, navigate to the /Components/Application subfolder.
The servlet example is ODA Online File Converter.
You can find it in the Drawings archive: Drawings_vc10_amd64dll\Drawing\Examples\Qt\OdaQtApp.
ODA Viewer and ODA File Converter are example projects that illustrate the possibilities of the ODA framework. They are free downloads that you can use to get an overview of ODA SDKs. If you are not an ODA member, you can use them for non-commercial applications only.
We do not distribute ODA File Converter; we distribute our SDKs which work with .dwg, .dxf, .dgn and many other file formats (not only read and save, but also edit, visualize, etc.).