I have had various joint and other injuries, as well as major abdominal surgery, so have been on various pain meds over the years. The non-opiate pain relievers that I have found most effective are:
Toradol - Had it post-surgery and I swear it was a miracle. It's like an NSAID on, er, steroids. But you can only take it for 5 days or your stomach falls out of your ass or something.
Mobic - Cleared up a majorly swollen knee due to Lyme disease and worked very well on the pain
Prednisone or other similar steroids
Relpax - migraines
In OTC land, 3-4 Advil can work. Aleve sometimes works on minor pain. I won't take Tylenol mainly because (a) it doesn't actually work and ( destroys one's liver at disturbingly low doses.