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One of them is a grass, the other is Duchesnea, or mock strawberry.

There are many ways to get rid of weeds, from chemical herbicides to boiling water. Start by boiling water, and pouring it directly on the spot where the weeds are growing. If that does not work, then you will have to use an herbicide, making sure to follow all instructions.

These articles will help: https://www.gardeningknowhow.com/plant-problems/weeds/using-herbicide-in-gardens.htm

https://www.gardeningknowhow.com/plant-problems/weeds/using-organic-herbicides.htm

https://www.gardeningknowhow.com/plant-problems/weeds/how-to-kill-grass-naturally-kill-unwanted-grass-in-your-yard.htm

These appear to be Duchesnea rather than strawberry, though it is very easy to confuse them. the taste will tell you. Duchesnea is bland and features a yellow flower, while strawberries (even wild ones) will have a white flower, and be, either, sweet or sour.

Unfortunately, Duchesnea is much more invasive than strawberry. Also, very unfortunately, what kills those will kill your Vinca.

I would look into keeping seeds from your Vinca for planting next year, then kill off your entire bed. You can do this by removing all plants by hand, then tilling, then pouring boiling water over the entire bed a few times per day for a few days.

These methods, combined, will kill off EVERYTHING in that spot, while leaving the soil viable for planting your new seeds next year.

Adding landscaping fabric before you add soil and replant will help with the weeding, but it is always best to keep them handpicked, when possible.

This article will help you to amend your garden bed for next year's planting: https://www.gardeningknowhow.com/special/organic/the-importance-of-soil-for-an-organic-garden.htm

Wild strawberry, whether Fragaria species or Duchesnea species, will be very difficult to control without killing your Vinca as well.

Starting over fresh, or killing everything will be the quickest method, though pulling by hand will be the only way to save your Vinca.

Here is an article that will offer more information on the subject: https://www.gardeningknowhow.com/plant-problems/weeds/wild-strawberry-control.htm

Make sure you have wild strawberries and not the mock strawberries, which have a yellow bloom instead of white. Most people don't want to encourage the yellow-blooming strawberry because even the birds won't eat it. And it will take over an area quickly.

Here is info on cultivating the white-flowered variety:
https://www.gardeningknowhow.com/edible/fruits/strawberry/growing-wild-strawberries.htm

A dewberry looks more like a raspberry so I wonder if you have mock strawberries growing? They flower yellow instead of white. Here are other possibilities:

https://www.gardeningknowhow.com/edible/fruits/dewberries/growing-dewberry-plants.htm
https://courses.missouristate.edu/pbtrewatha/indian_mock_strawberry.htm
https://www.gardeningknowhow.com/edible/fruits/fegen/what-are-brambles.htm
https://www.gardeningknowhow.com/ornamental/groundcover/barren-strawberry/barren-strawberry-growing.htm
https://www.gardeningknowhow.com/edible/fruits/strawberry/growing-wild-strawberries.htm

The best herbicide to kill wild strawberry is glyphosate. It is a broad-spectrum herbicide that effectively kills many types of weeds, including wild strawberry. Make sure to follow the instructions on the product label for proper application and safety precautions.

The way that I prefer, though, is to go natural! Boiling water, vinegar and, sometimes, even using beneficial creatures!

These articles will offer some way to get rid of your wild strawberries:

https://www.gardeningknowhow.com/special/organic/weed-it-and-reap-how-to-make-your-garden-more-appealing-without-chemicals.htm

https://www.gardeningknowhow.com/plant-problems/weeds