Route-->A map from Great Circle Mapper
That route fly's over Asia, so you need to pay for Asia, even if not stopping/transiting

For a start
No oneworld airline fly to/from RAR-->https://en.wikipedia.org/wiki/Raroto...tional_Airport
RAR is best a separate return from AKL.

No oneworld airline flys SYD-OSL direct. So needs to be SYD-XXX-OSL (2 segments). You need to determine that XXX airport. The OW RTW tool will not do that. Same with phoning. Will be many options, so you need to tell the phone agent where you want to go.
https://en.wikipedia.org/wiki/Oslo_Airport,_Gardermoen

Some of your other routes will need 1 (or 2?) transit airport. Example MEX-YYY-MEL. These are counted as a segments.