The meat tenderizer trick is a great one for removing blood stains. Think of the blood as a protein, which it is, and then recognize that meat tenderizers of any type will break down proteins. Something with papain or bromelain would be good. Those are plant based enzymes (although they may be synthetic) that work on proteins. It can work on older stains, but there are always some stains you can't get out.
Hydrogen peroxide from the pharmacy or grocery store bottles is fine for most clothes. If you have access to hair bleaching strength, don't use that on clothes. I can't think of any that it wouldn't be okay on. Medical people rely on HO to remove blood, vomit, betadine and other nasty staining stuff.
There are laundry additives that really do help remove crud. I use 'spray and wash' on minor grimey bits. My brother uses 'Lestoil' on greasy work clothes. I've used a 1:1:1 household bleach, laundry detergent and dishwasher detergent dissolved in a gallon of water combo for overnight soaking before, too. That's excellent on light colored clothes, but you do have to be careful around bleach, and know what you are combining. Any ammonia in the mix will release the suspended chlorine as a gas -- Toxic fumes.
Sometimes letting clothing soak in a washer with just the detergent will do the trick. Sometimes longer agitation, if you can reset the timer.
As far as funk from your gym socks, don't sweat it. :P If you don't overload the washer and all have a chance to circulate with an appropriate amount of detergent, they will come clean and relatively sanitized. Hotter water is more sanitary, but will set some stains you didn't pretreat and will wear your clothes out faster.
I'd be more concerned about the germs left from previous users than about gym socks tainting thongs.