Hello,

Vinegar burns the tops of plants. It doesn’t move to the roots and roots remain alive.. Hostas have robust roots and may resprout when their tops are burned back. Repeatedly burning the tops back will eventually kill the hostas. So will repeatedly clipping the tops off.

Here are some articles on herbicide strength vinegar: 

http://hyg.ipm.illinois.edu/pastpest/200714f.html

https://content.ces.ncsu.edu/are-there-alternatives-to-glyphosate-for-weed-control-in-landscapes

It would be best to dig as much of the roots as you can before planting anything else. Even if you kill the hosta  it would take some time for the thick roots to break down.

As aside note, consider digging the hostas and donating them to a local garden club plant sale, a neighbor, or Habitat for Humanity as free plants..