There appear to be more than one non-native/invasive plant in the photos, though their intertwined growth makes for concrete ID challenging. The plant with the compound leaves and thorny stems appears to be Multiflora Rose. While they are cousins to garden roses, they don't have flowers as showy, and may not flower at all if too young, too shaded, or periodically trimmed. As with some "climbing" plants, they are somewhat between a shrub and vine in habit, growing tall stems that hook or catch onto neighboring vegetation in order to grow higher and get more sunlight, rather than truly wrapping around supports the way other vines do.
https://extension.umd.edu/resource/multiflora-rose

Oriental Bittersweet does climb via twining, choking-out young trees and larger shrubs, but doesn't have thorns. The first photo seems to show growth like this, coiling around a larger stem we can't identify. Wildlife disperses the seeds of both this and Multiflora Rose, so easily could have deposited both weeds in these areas. Each is common in area woodlands and forest edges and is highly invasive. It's not likely any of these plants have grown under a house foundation - the soil there is too compacted and oxygen-deprived to be very amenable to root growth.
https://extension.umd.edu/resource/oriental-bittersweet

The groundcover visible in the second photograph is Wintercreeper Euonymus, which also happens to be a highly invasive plant. While this one is often deliberately planted as an evergreen groundcover, it is best removed so its seedlings don't harm wild habitat. If you are open to removing it, that may make dealing with this patch of troublesome weeds easier, as you won't have to avoid harming it. While it is not the focus of your problem, it could develop into its own menace once the competition is removed.
https://extension.umd.edu/resource/winter-creeper

The other hard-to-identify shrub/vine in the photo looks like one of the several species of non-native Honeysuckle (Lonicera) that occur in our area. These too are invasive and can take repeated efforts to remove.
https://extension.umd.edu/resource/exotic-bush-honeysuckles
https://extension.umd.edu/resource/japanese-honeysuckle

In lieu of herbicide use, repeated cutting-down of all growth for these undesired plants is needed to exhaust the root system. Trim them as close to the ground as you can, and be vigilant for removing regrowth as soon as it appears. This will be key to starving them of energy so they die as quickly as possible. Even so, it may take more than one year of intervention to see significant improvement.

If trying systemic herbicide, the smallest effective dose can be used if as much weed growth as possible is removed first. Then, the remaining stumps/branch stubs can be painted with herbicide, which will be absorbed and moved into the roots. Since this replaces spraying, it lessens the risk of accidental exposure to other plants in the area. Follow label instructions on any product you use, and expect to re-treat plants a couple of times if they return. Eventually, they will stop regrowing.

To keep new seedlings from appearing due to bird droppings or other natural dispersal mechanisms, consider maintaining a mulch layer over any bare soil, or by planting the area with native or non-invasive shrubs or perennials. When a patch of soil isn't available for colonization, weed problems usually decrease and are easier to manage.

https://extension.umd.edu/resource/invasive-vine-and-groundcover-control

https://extension.umd.edu/resource/invasive-shrub-control

Miri