It strongly appears you were shooting through a chain-link fence, chicken wire, or something else with a diamond-shaped pattern. Here is where I think the fence or wire would be (apologies for my unsteady hand drawing on a laptop trackpad):

The latest photo you uploaded shows even more distinctly what could plausibly be fence wire in the upper right corner, crossing diagonally across the sky in the background. In this photo, your lens appears to be further away from where the putative fence is (i.e., more chain links in the near field of view). Another poorly hand-drawn demonstration where I think the fence is:

The fencing would cause wavy lines parallel to the wires, that only shows up in the defocused areas of your image. In this thread at dpreview.com, user Tom Axford demonstrates how several narrow strips of paper held in front of the lens creates parallel wavy lines:

Out-of-focus background from dpreview.com discussion

Out-of-focus background with black strips held in front of lens

Now, the reason I think your entire background doesn't have wavy lines is because the purported fencing is a bit further from the front of your lens than the paper strips Tom Axford used to demonstrate the effect. Thus, the background region immediately surrounding each of the wires in the fence would demonstrate diffraction (the cause of the parallel wavy lines).