I am expecting to apply for the Canadian Experience Class immigration in Feb 2011. My post-graduate work permit expires May 2011. I am wondering, what methods will allow me to be able to keep working during the period before I receive a response for my PR application.
As Leon noted, your employer will need to apply for a labour market opinion (LMO). If the LMO is positive, you can apply for a temporary work permit.
Is there anything that allows me to keep working/staying in Canada during the period my application is being processed?
If you cannot obtain a positive LMO, then you cannot work. You might be able to stay on a visitor visa, but you cannot work.
Also, if I had to leave Canada, would my PR application be transferred to a difference office,
and affect the waiting time?