After having been illegal in the US for 8 years, convincing Canada immigration that you will not overstay a temporary work permit in Canada will be near impossible. You can however apply for your immigration.
Try the BC PNP at http://www.aved.gov.bc.ca/provincialnominee/strategicoccupations/healthprofessionals.htm and see if they can link you up with a job and get you an AEO so you can apply for permanent residency through BC PNP.
You could apply for skilled worker, see http://www.cic.gc.ca/english/immigrate/skilled/index.asp but you'd need to have at least 1 year work experience first.