the aspirin is fine. put it in checked or carryon baggage.
Your bag might be selected for inspection because of the powder (any powder, actually). Or it might be selected for inspection not because of the powder. Or your bag might not be selected for inspection at all. There is no reason not to put the oxiclean with you. If there was some reason I preferred to minimize the possibility of my checked bag being inspected then I would put the oxiclean in my carryon.