Phone (from within Canada): 1 888 242 2100
Phone (from outside of Canada [block caller ID]): 1 613 944 4000
I asked them to tell me specifically the lines I put there (visa office, medical, criminality, security, eligibility) as they have them in their system. Otherwise, they talk in general terms like "background check" like the EE portal does. "Background" = security+criminality, but if you ask specifically, they will tell you.
If you dial the 613 # outside of Canada, you can use these options (wait until it's ready to accept an option): 1 1 1. Then you'll get transferred to IRCC (the same as the 888 # inside Canada and you'll hear a male voice). Then you can use options 2 1 1 0 to get to an operator "fast" (it's the family sponsorship information menu tree but it goes to the same phone operators).
If you follow the tree normally to get info about your application, you'll have to enter your application number, date of birth, and listen to a long read-out of its status before you get to get in a phone queue, and 2/3 the time it will just say "we're too busy. call back later" instead of putting you in a queue.