Ellen:   Thank you for contacting the UVM Extension Master Gardener Helpline with your question regarding removal of burdock and Virginia Creeper.  

Burdock:

Burdock is a biennial that is spread by seeds during the second year of growth.  The first year, the plant grows from seed.  In the second year the plant develops flowers and seeds.  This completes the plant's life cycle and the plant dies.  The key is in removing the plant before seed production can take place.  Hand pulling the plant before seed production will work on smaller areas.  In larger areas, such as a pasture, mowing before seed production takes place is recommended.  Eliminating the plants will allow grasses to spread and reclaim the area.

I am attaching fact sheet links from other universities on burdock control.  Hope you find them helpful.

Identification and Control of Invasive and Troublesome Weeds in North Dakota | NDSU Agriculture and Extension

Spring Weed Control in Grass Hay and Pasture - Weed Management - Forages - Forage and Food Crops (psu.edu)

Managing Invasive Plants: Methods of Control (unh.edu)

I consulted with Ann Hazelrigg, Plant Pathologist at UVM, regarding your question on organic controls.  Below is her reply:

"Very tough weed to control...you can hand pull, dig up or repeat mow, but that still may not be enough.  The plant lives 2 years and the most important thing is you don't want it to produce seed.  Thousands of seeds can be produced at a time and they can live 2-10 years.  The best time to hand cut burdock is when it sends up the seed stock in the second year.  Cut the entire plant BEFORE the seeds are viable and the plant will die (which it would anyway, but it is not spreading more seed).  Probably easiest to dig when small and in it's first year.  Ugh..they are such tough weeds.  You can use Roundup or 2,4-D to kill them which you can apply just to the plant.  In some cases, this is the only way to get the weed under control, but you still may have seed coming up from previous years!"

Virginia Creeper:

Recommendations for removal of Virginia Creeper include pulling the plant by the roots, or cutting the plant close to the root and applying an herbicide to the cut area.  The same herbicides as listed above for Burdock are recommended, however, you may be interested in reading the link from University of South Dakota on organic herbicides.   As to your question on the vinegar solution, we do not recommend any herbicide not sold and labeled as an herbicide.  I also attached a study from the University of Maryland regarding the use of vinegar, which you may find interesting.  Note that when using any herbicides, look to make sure the specific plant is listed on the label, and be sure to follow all directions on the label.

PANHANDLE PERSPECTIVES: Wild cucumber and Virginia creeper threaten trees, shrubs | Nebraska Extension (unl.edu)

https://extension.sdstate.edu/organic-herbicides#:~:text=Organic%20herbicides%20use%2

Vinegar: An Alternative to Glyphosate? | University of Maryland Extension (umd.edu)

Control of Virginia Creeper also includes smothering the area with plastic and leaving the plastic in place to "cook" the plant in the hot sun.  Mow the area first, then apply the plastic.

Note that this plant has purple berries which contain seeds, so these should be removed to avoid the new seeds from germinating and creating more plants.

Just a caution:  Make sure the Virginia Creeper contains five leaves, and not three, as it is frequently confused with Poison Ivy!

I hope this information helps you in your removal effort.  Good luck to you!