@ang3ls I was also a humanities major, lol.
But yeah… you definitely need a detergent to remove soil from your laundry. Detergent grabs the soil and helps it stick to the water, so you can rinse it all away, leaving your laundry clean. Vinegar is just a very weak, diluted acid; it may help loosen some minerals, but without detergent in the water to help those minerals stick to the water and rinse them away, it may not actually do much to remove them. Baking soda is a base, so it raises the pH of the vinegar (making it less acidic), and I think they just break down into water and salts.
I’m not sure what baking soda even does as a laundry additive, but without detergent to wash it away when you’re done, I’d be concerned it might leave residue. It’s also a skin irritant for many people, so you definitely want to make sure it’s rinsed away.
Dish soap likely has similar ingredients to laundry detergent, but it’s formulated to hand-wash soil off of hard surfaces like pots and pans, whereas detergent is formulated to go in the washing machine to remove soil that’s embedded in fabrics. And you definitely want to use a product that’s appropriate for your washing machine, so as not to damage it. Hand-washing laundry with dish soap is probably fine in a pinch as long as it doesn’t irritate your skin afterwards, but don’t put it in your washing machine.
r/cleaningtips is a really really good place to learn. Also the website For the Love of Clean. But start by reading the use directions in your washing machine manual (and probably also read the directions on how to run a cleaning cycle, since you haven’t been using detergent in it for a while, and there’s probably some soil buildup in there). Then, buy a detergent and follow the directions on the bottle.
I’ll go ahead and warn you not to fall into the crunchy trap of substituting soap for detergent in a washing machine…
https://fortheloveofclean.com/laundry-love/homemade-detergent/