It's been a million years since I grew strawberries, but it my feeble memory seems to recall that you want sandy soil that drains well - they will rot pretty quickly in wet soils.
It's hard to tell from your pictures, but it looks like you may have a darker, richer soil there (which is great for your tomatoes & peppers). You might want to section off an area, dig out that in situ dirt, and get you some sandy, loamy stuff to replace it with.
I'm sure you know this already, but your cukes and squash are gonna spread like crazy - they take up a LOT of room.