Hi Jessica,
Thank you for your question about removing oxalis from your vegetable garden bed. As you have experienced, oxalis can be a very difficult plant to eliminate from the garden.

Oxalis flowers and produces seeds heavily in the spring and summer but can produce both all year long. Small plants can easily be handpicked or dug as they appear before they flower or form seeds. Removal of all vegetative portions of the plant, including roots and rhizomes, is important. Rhizomes can be easily removed when the soil is moist. Do not place the weeds with seeds in compost bins for reuse in the landscape.

A light layer of mulch in landscape beds and around flowers and shrubs will aid in preventing further germination of oxalis seeds. The seeds require light for germination, so limiting light to the seedbed with mulch will reduce the numbers of new oxalis plants.
Source: Oxalis Control | Home & Garden Information Center (clemson.edu)

If you need additional information, I recommend you call the Deschutes County OSU Extension office in Redmond at<personal data hidden>. Ask to speak with Amy Jo Detweiler (oregonstate.edu), a member of the Horticulture Staff. Amy Jo welcomes your home garden questions and is a great resource.