Odin is perfectly compatible with common source control systems. There are however, a few things you may want to ignore.
If you're using Odin's serializer and are building to AOT platforms, then it's advisable to ignore the contents of the Plugins/Sirenix/Assemblies/AOT folder, as this may contain generated .dll's for AOT compatibility that you do not want to track in your source control system. This is, however, mostly a question of preference.
All of Odin's demos are located in unitypackages, so users can at anytime unpack them and have them locally on their machine. So there is no need to include the unpacked demos in your repository either.
If you have a .gitignore file located in the root of your Unity project, then simply add the following lines to ignore the files mentioned above, remembering to adjust the file paths if you've moved Odin from its default install location.
# Ignore the auto-generated AOT compatibility dll.
/Assets/Plugins/Sirenix/Assemblies/AOT/*
# Ignore all unpacked demos.
/Assets/Plugins/Sirenix/Demos/*
# But keep the demo packages themselves.
!/Assets/Plugins/Sirenix/Demos/*.unitypackage