In my experience, the powder will not eliminate serious stains when simply added to the wash, but I have found that it works really well reviving dingy whites and getting out serious stains if you are willing to let the item soak for a VERY long time. I had a vintage christening gown that had really yellowed with age and would obviously not stand up to chlorine bleach. I put it in a bucket with a scoop of oxygen cleaning powder and enough hot water to cover it, and just let it soak for several days; it came out as white as new with no damage to the fabric. I've had good results against serious stains (ground in dirt, blood, body soil) using this method, but N.B. it can dull the colors for anything not truly colorfast.
HTH,
-Z