If court found you guilty, I would say you have no chance to stay in Canada and you have to leave Canada, but after five years you may apply for pardon and then for PR again.
About "apply for H&C or refugee".
1. If you apply for H&C and IF even you get first stage approval (before leave Canada) : then anyways on stage 2 CIC will check you background and find criminal inadmissibility - case should be rejected.
2. If you apply for refugee, 0.00001% chance that IRB will even process you case after DUI and PR rejected. Should happened something very big and bad in your old country (between right now and when you applied for PR) to process your refugee application.
You can try to appeal your DUI court decision with very good criminal lawyer, some time lawyer may to prove to judge that you drive that car because you did try to safe your life or another life an was not any other way and etc.... (90% to just loose money ,very hard to prove) and if you win case then you may ask CIC for Canadian Mercy.
Also you can try political way (MP) but before go to MP you have to have lots of support letters from Canadians and again you have to explain "why you got DUI". This case you go use together with something else. And for sure depending who is your MP (Liberal, NDP or Conservative). Only if Liberal make sense to go then.
Anyways I suggesting to find good lawyer (criminal first) .
Regards,
DHUdson.