I have read pretty much everything I have in my own resources and everything on the internet in relation to getting rid of Oxalis in the home garden, and none of it gives much hope unless you just have a small patch that hasn't spread much.  God help you if you do what I did and unwittingly rototill this plant into a large area. 

When I moved into my house, I had a few small patches of the stuff.  I actually thought it was a pretty little plant and that I was lucky to have inherited it.  It was mostly in the lawn and didn't seem to spread too much, probably because of regular mowing.  Then I decided to create a fair-sized island bed and I tilled under all the grass and Oxalis.  I proceeded to spend a good bit of money on edging this bed with terra cotta blocks.  Before I was even done with the edging blocks, I knew I had a big problem with Oxalis, as it almost immediately overtook the whole area.  It was fall at this point, so over the winter, I pulled what I could and then systematically smothered the whole area in up to a foot of mulch.  I probably hauled in 60 bags of the stuff.  Spring came and some of the Daffodils had trouble pushing up through all that mulch, but it didn't phase the Oxalis.  Above is a picture of a Hyacinth flower struggling to push up through the Oxalis in April (there is also some ground ivy on the right in this picture, another persistent weed that I constantly struggle with).  Even strong plants like Liriope were being muscled out and were looking sickly. 

Finally, I had enough and I went to the store and got some Roundup. I don't normally use Roundup but it was worth a shot in this case.  I decided to do a test first before really getting out there and doing some damage so I picked a clump and painstakingly painted the Roundup onto each individual leaf with a paintbrush.  The next day I went out there and indeed, the leaves I painted were wilted, but the few I missed were fine and dandy, meaning that I killed the leaves but it didn't affect the bulb at all.  Two days later it had sent up replacements. So forget it - unless you have absolutely nothing else in the garden and you are willing to soak the ground with a chemical, Roundup won't work. 

Next step was to take a weekend and get out there with some thick gloves and start pulling.  One thing I will say for the mulch - it does make pulling Oxalis a bit easier.  You can't just break the leaves off - you have to go for the bulbs.  If you get the lateral roots (the top bulb with the whitish icicle things), you will slow it down, but ideally, you want to pull up the whole plant, bulbs and all, as in the picture to the right.  After much trial and error, I find that it pays to take the time to find the source of the clump.  Look under the leaves and try to determine the central source for the stems, then dig down in that area with a glove on and try to pull the whole clump.  After my weekend, my garden looked 100% better and indeed, I did slow it down some after putting a pile about 5 feet long and 2 feet high at the street for pickup.  Of course, victories are limited with Oxalis - a week later it was back, but not quite as strong.  Right up until today, I try to get out there and do 30 minutes of Oxalis pulling 3-4 times a week and it is indeed making a difference.  I have a good number of happy flowers and herbs that are only slightly bothered by the Oxalis at this point.   I keep a close watch and if the Oxalis is encroaching too closely to any weaker plant, I go for it before it gets bad.  Even just snipping the leaves will help weaken the bulb over time, so don't worry if you miss the bulb at times.  You will always have another chance at it.  For me, this will go on for years, but essentially, I have reclaimed my garden, and I hope eventually to have the Oxalis pulling down to maybe a weekly session. I do continue to add mulch regularly, as the mulch has done so much good for everything out there, and at this point, it does seem to be helping in slowing down the Oxalis to some extent.  I don't, however, expect I will ever be completely rid of Oxalis no matter what I do, unfortunately.  I can only hope to keep it at bay where it's not a threat to every desirable plant in the garden.

So that's my story.  The only way I know of to get rid of Oxalis is by hard work, but in the end it's worth it.  An infestation of Oxalis will eventually overtake pretty much everything else out there, so my advice is to just get out there and enjoy the solitude and revel in the little successes - and never, never till that area again!

UPDATES:  Below is the garden in mid June - I have made headway.  There is still some Oxalis out there but with regular pulling it is a minor annoyance at this point. 

Below is the garden in October - with the cooler weather I am seeing more and more Oxalis, but it's still only a nuisance rather than a crisis.

Here we go again.  Oxalis loves the cold, and the garden in January needs a thorough weeding again.  Below is a wide angle view, with a view below that of how thick this weed becomes in a hurry.