you actually have some good time for you to complete all the formalities.
1. if oath is on 15th, you can apply for passport on 17th. a trick here is constantly keep checking your application status in cic, the moment anything changes on that information, it means that passport canada has recieved your information and you are good to apply.
2. passport canada accepts applications only mon to fri
3. for urgent processing, you can get the passport within 24 hours, but, you have to apply at a passport canada office only (not post office-mail in etc)
4. you can recieve the passport on monday 20th,
5. you will have time to apply for a indian visa on arrival - its online
now the tricky part,
overall - you have sufficient time to get your canadian passport, however, you may not be left with enough time to get a indian visa.
here is what i did for a exactly - well almost - similar situation i was in.
i applied my passport on thursday, got it on monday morning - 10 am, and had a flight to catch to india at 1 PM on the same day - monday.
went to india on indian passport, after reaching india applied for an exit permit, came back on canadian passport showing the indian exit permit
the whole thing is very painful though - no one knows the process - so pretty much you have to do it on your own and guide the people on what they need to do:
references :
1. 3 month grace period to travel on indian passport - here http://www.cgitoronto.ca/content/surrender-certificate-0 - go to the end of the page
2. process to get indian exit permit here https://indianfrro.gov.in/frro/menufrro.jsp
hope this helps and btw - congratulations
cecapplied