If you keep the roots from freezing, you can easily proagate your oxalis that way. That is a very unusual cultivar! More common ones are widely available now in garden centers, sold as shamrocks. Here is a link that might be useful: indoor-outdoor oxalis

They have a deep white carrot like tap root, above that they have a cluster of bulbs that look like elongated Lilly bulbs, the tops grow from a central crown, leaves have 4 petals, there are several verities-ranging from green to purple leaves, and small multi flowers on single stem. The different verities range in size of 1/2" across the leaf to 2", in height the different species range from 3" to 12". A goat will eat it, and cheaper yet build a chicken tractor and put 4-6 hens in it and move it around every day. But, any animal will only eat the tops off and not the root. I've grown these plants in pots for 35 years and found that any extras can simply be stored in their pots for 2-3 years without water. Then simply put back in the greenhouse and watered and they grow like weeds. They can survive excessive watering and no water for long periods of time. If you are trying to eradicate it, you can try the black plastic--but, short of removing all (every last tiny scape of root) is the only way to get rid of it besides using a herbicide. I have a friends in Orange County, California had it growing next to a concrete sidewalk and redesigned their landscaping, they removed the sidewalk and all under it were bulbs from these plants. Their landscaper used round-up on them, said if they didn't dig and haul away all the bulbs and surrounding soil (to make sure even the tiniest bulbs were removed) that it was his experience they would be a constant problem.

I have oxalis. All around. The green with purple flowers. If they weren't so annoying, I would probably like them. and wait a minute! While I was trying to figure out my other hated weed, I found out it, too, is oxalis. It's a much smaller leaf, with small yellow flowers. I also fight with rattlesnake weed (Florida Bettony). It grows much like the previously mentioned, only it's roots and tubers grow further down and are much more fragile. We also have vines. Lots and lots of vines. Many of them have thorns. Fun stuff.

It ain't gonna happen! That is one plant that even seems to grow in the winter. Actually, if you let the Creeping Charlie, violets, Dayflowers and Lady Thumbs take over instead, you might get less wood sorrel. LOL! However, I do find it is one plant easy to pull out with a metal rake or other standing weeding device. Keep at it and try to get it before it flowers. Maybe a germination suppressant like Preen if you aren't looking for any self sown plants. Keep applying new mulch. Use low groundcovers like sedums to compete with it - you will still get some growing inside the plant. I think I've lessened the amount of wood sorrel I have in my yard a bit over the years but I know I will never get rid of it. It is always ready to increase in numbers. I actually like the look of wood sorrel so when a volunteer plant appeared under an indoor tropical plant once, I let it grow groundcover-like. It actually looked cute until it started dispersing little black seeds all over the drapes and walls. Once I decided to start pulling it out, I couldn't get rid of it and we are talking about just an area of one indoor pot. I am guessing it resprouts from roots left behind. If your problem is that bad, you might try digging up your plants and see if that suppresses the regrowth at all.