Q.How can you get rid of Jewelweed and False Nettle. They are both taking over my woods and garden!
Both grow in open shaded areas, ie, in the woods or under plants in rich soil. Butterflies and bees seem to like Jewelweed but the plants are extremely invasive on my property and killing off other plants in the woods and in my garden.

Organic and/or conventional foliar herbicides aren't very effective against jewelweed simply because its succulent foliage causes these water-based products to bead on the leaf surface, preventing the product from getting absorbed and taking effect
Since jewelweeds are annuals, a few simple steps will cut down on their population significantly. First and foremost, do not allow them to go to seed. Either weed wack them or pull the plants out before the flowers open so the seeds can't spread. Thankfully, you'll find them to be shallow rooted and quite easy to pull out with nothing more than your hands
This article will help with Dead Nettle control.
https://www.gardeningknowhow.com/plant-problems/weeds/purple-deadnettle-control.htm