1. Being out of status in the US will not affect your chances to immigrate to Canada but it would be very hard, if not impossible for you to get any kind of temporary visa to Canada with your history of overstay in the US.
2. You can not have your application processed in the US because you were not legally admitted to the US. You can still stay in the US while your application is being processed in your home country. You would only have to return to your home country if the visa office there requests an interview.
3. If you apply under the skilled worker program, be prepared for a year, could be longer. Could also be less than a year if you have a job offer.
4. A job offer should speed up the process but will not allow you to apply from the US.
You can read about AEO (arranged employment offer) at
http://www.hrsdc.gc.ca/eng/workplaceskills/foreign_workers/supperimm.shtml The employer would have to apply for this and send it to you and then you can use it to apply for your immigration.