A lot depends on the quality of the dirt. I am not a big fan of landscape fabric except to use under a decorative stone, but I not a fan of decorative stone either.

Its kind of late now, but the first step is in the fall when you can use a herbicide like Round Up to kill everything. But now, I would suggest that you wait till spring and then remove the sod with a sod cutter, then till when the ground is dry enough. Wait three weeks and then till again.

Each time you till, you will fluff the ground up, after the second tilling, take about half your new topsoil and compost and till it into the ground. Rake the soil from around the edges toward the center down to ground level, then set up your raised bed. Smooth the soil and add the rest of the top soil and compost.

At this point, I would keep the herbs in their pots as long as possible, maybe even repot them in larger pots. Let the soil in the bed rest for a bit and see if any weeds pop up. After another two to three weeks, most weeds should have germinated. Scrap(e) them from the top soil. do not scrap(e) very deep, no more than 1/2". If you go any deeper, you will drag up new seeds to germinate. Then plant your herbs.

Same for the strawberries.

I think by following these instructions, the soil in the bed will have better contact with the ground so it will wick up moisture as needed. It will still need water once a week or so, but it will help to keep the topsoil in the bed from drying out so quickly. It will also help temper the soil temperature. If you isolate the topsoil, it will be subject to drying out more quickly, flooding too quickly and greater fluctuations in temperature.