Oath time seems random to me. There are people who get it within same day (at the same test centre - for instance there are people in Oct 2018 Scarborough who got oath next day of test while others waited for 5-6 months).
Without pr card I don’t think you can take your test. they check pr card before you take test. My advice would be to contact the call center and get their feedback as to the next steps... not sure but you may need to get a new passport and a pr card before you can appear for test. All the best