I've had great success with using ammonia (1 cup) in the washer for removing oil stains, yellowing and deodorant buildup (white pasty streaks at the underarms). Warm/hot water, a bit less than normal soap, lemon scented ammonia. MAKE SURE YOU ABSOLUTELY DO NOT EVEN THINK OF ADDING BLEACH - DANGEROUS WHEN MIXED WITH AMMONIA. Could even do a soak of the clothing in the washer - throw in clothes, add water and ammonia/soap, and then let it go through the washing agating part and then stop the cycle before it drains for the rinse stage, and leave it to hold with that for a few hours before commencing the rest of the cycle. I can do this simply by leaving the lid up, but newer washers may be annoyingly weird enough to not allow, so just try soaking in bucket/basin with a bit of stirring around over an hour's time, and then dump the whole thing (water mix and clothing) into the washer to complete.
Best part? No scrubbing or massive amounts of stuff to mash/mix/measure. This is for fresh stains, but honestly I've seen improvement with older stuff but I can't tell you with certainty that it will 100% work on older stains. But it's cheap and easy, so might try it anyway. Soak in hot/warm water for an hour and then wash and fingers crossed.
For the coffee/tea stain, I'd suggest using the dish soap/baking soda mix and let it sit/soak in that with small bit of hydrogen peroxide in the water in a small tub/bucket/washing machine basin for a few hours. Be aware that hydrogen peroxide may cause bleaching in some fabrics, but likely you'd not be wearing the items anyway with bad stains, so may risk it.
I use a half cup of ammonia in EVERY wash now it's so great about stripping all the oily mess/deodorant out of our clothing and reduces the need for the "regular" amount of soap as well. I buy it in quart jugs from the dollar store in a lemon scent and it's lovely - if you REALLY tried and buried you nose into the fabric you may detect the faintest whiff of lemon... but it's similar to using vinegar in the wash but somehow better since I'd been a long-time user of vinegar and my towels still would smell slightly musty and it wouldn't even touch the deodorant.
Oh! And I now wear an apron any time I am working in the kitchen with any cooking oils. I am shocked at how long it took me to realize that that is where the oils dots on my shirts was from. I have some really awesome aprons now tho, and I also make sure to change into bumming around the house clothing that I don't mind getting spattered if it's going to be a really messy meal prep, but ammonia so far has been amazing if I forget both apron and changing.
