Which themes work with the Oxygen Builder?

None. Oxygen is a theme-less page builder. Once activated, it nulls any theme in use:
  • The theme’s style and a scripts are not loaded automatically.
  • The theme’s functions, hooks, and filters are no longer accessible or executable.
But it doesn’t meant that you can’t have access to pre-built designs. Oxygen has what we call Design Sets. It’s pre-built designs organized as full pages or sets of elements that can be loaded from within the builder (under Library > Design Sets.) Oxygen’s design sets library is growing steadily by the Oxygen team and others: