What many call "weeds" are really wild flowers and many of these have root systems that can keep growing the plants unless they are eliminated as well as the above ground parts of the plant. That you have tried Lily of the Valley and Pachysandra with little success indicates there may a soil problem that needs to be corrected, so a soil test is in order.
Lily of the Valley will grow in most any soil but they prefer a soil well amended with organic matter that is near neutral, or like most other plants in the 6.2 to 6.8 pH range.
Pachysandra likes the same type of soil but prefers a lower soil pH.
But have a good reliable soil test done to see what you have, because many of what we call "weeds" do prefer a soil that is much leaner and meaner than that which most of the plants we want to grow do.

Haha - I had a similar problem. There is a rich soil area full of recurring vines, tree saplings, and gets littered with hickory nuts in the fall (which inhibits growth of some plants). My solution - I planted tall, woody shrubs and fruit trees. The "weeds" keep the soil rich, while the understory plantings thrive as well.

Some tall ornamental grasses are aggressive as well.

This post was edited by river_city on Sat, Oct 12, 13 at 8:34