Please help? I've heard US citizens don't have to have visa to live in Canada. Is that true?
I'm reading all kinds of articles and information on the web but still didn't find the correct info.
No - that's not true. US citizens don't need a visa to VISIT Canada. However if they want to live there, that's a completely different story.
You should start reading here about the different immigration routes available to see if you and/or your girlfriend qualify:http://www.cic.gc.ca/english/immigrate/index.asp
There is no PR fast-track for Americans. You should decide who is going to be the primary applicant based on who has enough points to qualify for immigration. If you apply to immigrate to Canada as the primary/only candidate, there's a chance you will have to return to your home country (if an interview is required, it will be held in your home country - not in the US).
I assume you've been illegal in the US for more than a year? If so, are you aware that you will be automatically banned from the country for 10 years as soon as you leave? Have you considered marrying your girlfriend and attempting to adjust your status in the US?