Perennial weeds

In order to eradicate problem weeds, including Nut Grass, Onion Weed, Sour-sob (Oxalis), and Tradescantia (Wandering Jew/Creeping Jesus), it is necessary to understand how these plants reproduce, because merely digging, or pulling out, these weeds is rarely successful.
Wandering Jew or Creeping Jesus is a weed of moist, shaded places. It produces extra roots at the stem joints where they touch the ground. The stems snap easily when pulled, allowing small pieces of stem to remain in soil and produce new plants, making it difficult to completely eleiminate in one go.
You can tackle this weed by whipper-snipping or cutting off as much above ground growth as possible. Rake it up and dispose of it in a sealed plastic bag. Then cover the area with black plastic or weed mat anchored around the edges. It likes damp soil, so the black plastic is best – it will prevent rain getting to the soil. Excluding light also prevents the plants from manufacturing food for future growth. Then, the most important part is to go around the outer edges of the plastic with a sharp spade and cut through any underground runners that may be extending beyond the plastic, otherwise these parts will keep supplying the runners under the plastic with food and moisture to grow. It can take up to a couple of months to kill off this weed.

Nut grass, onion weed, and Oxalis or Sour-sob release small bulbs (bulbils) into the soil when plants are pulled out, or when soil is disturbed by digging, which rapidly increases the number of weeds. During each growing season, these weeds use sunlight, carbon dioxide and water to manufacture glucose to use for energy. The glucose is stored in the bulbs and bulbils during a period of dormancy to be used for growth in the next season (in the same way as spring flowering bulbs).
The way to eliminate this type of weed is to prevent them manufacturing food through the green parts of the plant. This can be done by excluding light and water for a couple of months with thick cardboard or black plastic. If these weeds are a problem where they are close to plants, repeatedly cutting off the foliage at ground level will eliminate them.
If they are growing in a lawn area, improve fertilisation and watering of the lawn. A healthy, vigorous lawn will smother these weeds.