I have been able to import contact into 365 from Outlook 2002 but by exporting the original data into a .csv file. The suggestion in para 3 above to export from 2002 as a .pst file is not supported for import by Outlook 365. I would also like to have been able to import my 2002 calendar but that appears not to be possible at the 365 stage.
I have to say that I am disappointed that 365 does not offer .pst import capability. Hopefully this will be added in future upgrades. Are you able to pass these comments on to the developers?