In a former life I graduated with a degree in chemistry....
so- first off, Muriatic acid is not sulphuric acid, it's hydrochloric acid. That's an important distinction because muriatic acid gives off Chlorine gas as fumes when it reacts with calcium carbonate. Obviously you don't want to be breathing chlorine gas so all acid baths must be done outside wearing a gas mask suitable for acid.
Second- Vinegar is not gonna do much at all because it's an extremely weak acid.
Third, yes an acid bath will slightly eat the rock itself but to such a minor degree as to be unnoticeable.
Fourth- an acid bath WILL loosen and possibly dissolve organics from the rock so I think it's quite valuable to do. J
ust grab a big bottle of muriatic acid from Lowes/HomeDepot and a big tub. Put the tub outside on rocks or soil because it will likely overflow. (don't put on your driveway, it will etch it!) Fill the tub with water and put the rocks in. Don the gasmask and slowly add acid to water (never add water to acid!) until it's doing a good frothing and bubbling. Then walk away for an hour or two and let it do it's thing. In an hour dump in a big box of baking soda (not baking powder!) to neutralize acid and wash, wash, wash the rocks until there is no more reaction to the baking soda. I would let the rocks sit overnight in water too but eventually the acid will be gone and the rocks will be as clean as a rock can get.