A weed mat mulch proved effective in reducing the number of oxalis bulbs when used over two years in reseach conducted by AgReserach, Hamilton.
Soap sprays are said to be effective, although this was not supported by the above research. However, if you wish to conduct your own experiment, here is a recipe for soap spray:
Use soft soap (made with potassium carbonate and not caustic soda) Dissolve 50g in 4.5 litres hot water. Apply when cool.
Oxalis is difficult to control because it produces small bulbs which spread through the garden easily, but they are usually clustered and not very deep so can be carefully dug out.
However, it may be that your oxalis problem is not such that it greatly reduces your yields or causes that big a blight aesthetically. Some choose just to live with it.
For some general advice on weeds see gardening author Jackie French’s website:
Here are some methods I've used over the years for oxalis. Ducks like to eat the bulbs (I've cooked and eaten them. They're starchy and delicious but really too tiny to harvest except as a novelty). Let the ducks into the garden after the bulbs are tilled. Black plastic for a long time( at least one year) will wipe them out. Tall and dense cover crops out compete them and oxalis is a great living mulch in the California climate. It grows during the wet season when many plants are dormant then dies out during the main growing season.