For some bizarre reason, Epsom salts has gotten some sort of reputation as a garden cure-all. A huge myth!! Epsom salts can be used as a soil amendment but is really only effective if you have a magnesium deficiency. But it is not a herbicide and will have little effect when used for that purpose. Just an FYI, but all fertilizers, including magnesium sulfate, are only accessible to plants when they are in the form of a soluble salt.....like the Epsom salts (magnesium sulfate). That is very different from using table salt. And using table salt - sodium chloride - on the garden is a big no-no!! It contaminates the soil and can make it difficult for any plant to live. If you over-apply a fertilizer salt, you can get burning or plant damage but that is a far different response than a herbicide.

Vinegar is used as a herbicide but does not kill roots. And it will not distinguish between a weed and your lawn so expect some damage to the lawn if you use any vinegar to control weeds.

To be perfectly honest, most organic weed controls are not particularly effective. Boiling water works well and vinegar also works well on shallow rooted annual weeds but will have little effect on deep rooted perennial weeds (like dandelions). And none will distinguish between a weed and a more desirable plant. The best organic control for weeds in a lawn is growing a very thick healthy lawn and hand pulling what weeds may pop up.

Vinegar, but not the usual salad dressing stuff, at 20 percent Acetic Acid will kill most unwanted plants, aka weeds, but the only thing soap might do is make the spray a bit more fluid because the soap will reduce the surface tension of any water in what ever is in the mix. Epsom salts will do nothing to kill any plant.

Epsom Salts are Magnesium sulfate of about 10 percent and that is a mineral plants need to grow, so spraying Epsom Salts on plants is supposed to help them grow. However, at about 10 percent Magnesium sulfate and then diluted with a lot of water there would not be enough to make much difference. Save money by not using any in the garden.

Most web sites I have seen about this "natural" weed control lists Dawn Dishwashing Liquid as the soap to use. Note that the manufacturer, Proctor and Gamble, does not use the term soap for this product because it is not a soap. It is a synthetic product made from petroleum byproducts and therefore not an acceptable product for organic growers to use in the garden.