Will vicodin, oxycotin 80, and norco (hydrocodone and acetaminophen) show up as the same thing on standard urine test?

No: Norco (hydrocodone and acetaminophen) and vicodin are the same and are detected by the test for "opiods" which actually assesses for the presence of hydromorphone. Oxycontiin (percocet/Roxy) do not break down to this and a person using these will test negative for opiods. One has to do a test for oxy which usually is looking for the Oxymorphone metabolite. Sounds similar but chemically distinct

Yes: In a standard urine drug screen they will show up a positive for opiates. There are more complex tests that can be done that will break down which drugs you've taken.