It's pretty well impossible for you to get a temporary work permit in Canada with a 12 year overstay in the US on your record. You can however apply for immgration to Canada without a problem. You need to get arranged employment (AEO). First you need to find an employer in Canada and convince them they need to hire you. They need to apply for an AEO in your name to Service Canada. They send you the AEO when they get it and you use it to apply either for FSW category 2 immigration if you have enough points or PNP immigration depending on the province.
Since you were not admitted to the US with a 1 year visa at any point, your file can not be processed in the US. It would have to be processed in your native country. If they request an interview, you would have to go there. They may not request an interview. It depends. You deal with CIC mostly through the mail (unless they request an interview) so you might not have to go there. My file was processed in London and I never had to go there.
It is very hard to get a job offer without being there yourself and being able to do interviews, even though there is absolutely no risk for the employer and they are not even bound to hire you when you get PR.
Read about immigration options here:
http://www.cic.gc.ca/english/immigrate/index.asp and about AEO's here:
http://www.hrsdc.gc.ca/eng/workplaceskills/foreign_workers/supperimm.shtml