Acetaminophen is widely known as the strongest over-the-counter pain reliever. Acetaminophen can be taken up to 1000mg at a time, every 4-6 hours. Stronger pain relievers can be requested from a physician.
I would say the the strongest over the counter pain medication is Aleve. You can take up to 2 aleve at a time. Aleve always works the best and it is in my opinion the strongest.
It depends on the doasage of what you take, as well as how your body responds. Many people find ibuprofen at 800mg doses (the equivalent of 1 prescription strewngth pill) , not to exceed 3200 mg /daily and only for a limited time to be quite effective. However, I personally have found 2-3 Aleve at 1 time to be better.