As you suspect, you cannot become a citizen while on parole or probation.
http://www.cic.gc.ca/english/citizenship/become-eligibility.asp#criminal
As you are checked in for the Oath, the officer asks if you have any criminal issues. You would need to answer yes. Even if they don't ask, you need to volunteer this info.
However, I would strongly suggest sorting this out beforehand and speaking to a professional (either a settlement worker with whom you can consult for free or a knowledgeable lawyer, which will not be free). They could give you a sense of how your case will go forward and any issues to be aware of when informing CIC and beyond.
They may suggest that you call the Call Centre and/or inform CIC in writing before your Oath date.
While this doesn't apply to
unknownperson101, other PRs with criminal issues who may read this should know that
any PR charged with a crime absolutely needs to consult a lawyer who knows about the immigration consequences of criminal convictions. Sometimes criminal lawyers will advise clients to take plea bargains or plead guilty without realizing that their client could get deported (PRs sentenced in Canada to prison for 6 months or more for a crime can be deported). See this pdf for more info:
https://ccrweb.ca/files/criminalitybackgrounderen.pdf
Your instinct to be straightforward and honest with the CIC is a good one. You definitely need to do so, due to issues regarding misrepresentation that others have mentioned, but you would be wise to speak to a professional first.
Good luck to
unknownperson101.