Hola,
I'm no expert, just take these as opinions from a Latina who also needs a visa to visit Canada

(btw, my husband is Canadian)
It's hard to say whether she would get the visa or not, you'll have to try applying and see what happens.
How long have you been living together? If more than one year, it counts as "common-law partnership" (even when you're not sponsoring her for residency) and the visa officer might be more flexible. You can probably attach some proof of this like the apartment's contract with both your names.
About your questions...
- Her passport... if her over-stay in Europe is stamped on her passport, she'd better get a new one and do things "fresh", just to be on the safe side.
- Letters of invite... YES, try attaching 2 or 3 letters from Canadian citizens or Perm.Residents residing in Canada. The letter from your family (parents, if possible) could state something more "emotional" like: "we are really looking forward to meeting (GF name) because we know that she's an agreeable, honest and responsible partner to our son; and we expect to enjoy time together as a family. She will be with us during her whole stay in Canada". [well, this is an example... make sure that her itinerary matches what they say]
- Your bank statement and work contract... I'm inclined to think they're not necessary because it's HER visa, not yours. But perhaps writing a letter by yourself and attaching a bank statement wouldn't hurt.
Mucha suerte!