Put as your mailing address whatever address would be best for getting mail. The residential address can be the address you are at now - you are a visitor in Canada, but still living here. You could also use your permanent address in your home country. If you do, you should explain that it is your permanent address, but that you are here in Canada as a visitor.
If you are applying as a common-law partner, it is better to use the Canadian address as the residential address. You have to prove you have lived together for 12 months. Many forum members have used the address they were staying at in Canada as their residential address, even if they were applying outland, with no problems.