I'd suggest the following:
1. Find a suitably sized bucket and some rubber gloves.
2. Get some oxygen-bleach rich powder detergent. If you were here I'd say normal Ariel or Persil Bio. I'm not sure what the equivalent of that is in the US, but I am sure some of the more traditional Tide powders with bleach are possibly quite similar.
3. Fill the bucket with hot water and add plenty of the detergent, give it a good stir.
4. Add the clothes and ensure they're completely saturated.
5. Leave overnight to work its magic.
6. Place the clothes directly into the washing machine and run a long cottons cycle at the highest temperature the machine will do and that is safe for the clothes.
7. Select the prewash cycle (if this exists over there) as it will give them a short wash first which will rinse out the detergent solution from the bucket and then add fresh detergent from the drawer which will be more chemically active for the wash. If you don't have this option, run the machine on a short rinse and spin first. Then do the cotton's cycle.
If you were on this side of the atlantic, a 90ºC (195ºF) cottons cycle with a prewash option might remove them with oxygen-bleach detergent, but those high temps can be a little harsh on clothes if they're not pure cotton or have any kind of synthetic threads in them that won't cope well with boiling water. For towels and stuff like that they're fantastic though.
I have had excellent results with very stained clothes on a 60C (140F) cycle with either Ariel or Persil powder. The liquid versions aren't as good at shifting this kind of stuff.
Back in the 1960s-70s there used to be a product called Napisan which was specifically used for this purpose. You put it into a covered bucket and left cloth nappies (diapers) soaking over night and it basically dissolved away all this stuff. AFAIK it was just a powder with loads of oxygen bleach and enzymes.
---- edit ----
I had a look at the ingredients of Tide's products and most of the powders have nothing like the cocktail of enzymes you'd get over here.
I'd suggest using a top of the line liquid detergent and an oxygen bleach in the same soak process in that case.
You should be able to buy an oxygen bleach stain removing additive in most supermarkets I would assume. Most of them are just Sodium percarbonate based products that release a peroxide during the wash.
I was looking at Persil bio for example:
Enzymes: Mannanase, Amylase, Lipase, Subtilisin
Bleach : Sodium Carbonate Peroxide
and the detergent aspects of the formula are very complicated.
The liquid version has: Mannanase, Amylase, Pectate Lyase, Subtilisin