The Edmonton Sexually Transmitted Infections (STI) Clinic 11111 Jasper Avenue has STI testing available as well as condoms
The Ross Armstrong Centre/HIV Edmonton Office has STI testing available and has self testing kits for HIV
The Emergency Wards at the University of Alberta Hospital, Misericordia, Grey Nuns and Royal Alexandra Hospital all have rapid HIV testing available
The Birth Control Centre/Seventh Street Plaza has birth control methods, including condoms, as well as STI testing, pap testing, and HPV vaccines
There are plenty of pharmacies in the city I live in, most of which have plan b available. There are also plenty of medicentres in the city that offer STI testing, listing all of the pharmacies and medicentres on this particular forum may overcrowd it as in doing my research I managed to find over 20 pharmacies and over 50 medicentres in the city, but I am planning on keeping a list of them handy for myself.