If there is a single string which runs in a triangle through two eyes (one each side of the picture) and across the hook/nail, then it may have slight kinks in it at these three points.

So when you adjust the pictures slighty, they move to where the kinks are.

Try sliding the string or wire around by a few centimetres to use a "fresh" part that hasn't been kinked by the weight of the pictures, which you commented are fairly heavy.

To make them level, you'll obviously have to slide the string/wire across the hook to obtain a level position.

Maybe the pictures really are level, but their subject matter creates the illusion that they are crooked.

The hook marked in green has a ribbed top edge.

Adjust the position of the picture so the nail is located at one of the indentations, so it hangs level.

If it droops one way on a particular groove, and the other way on the next groove, then you need to counterbalance the picture.

You can do this by attaching a weight, such as a clean nail, to one of the clips on the left or the right of the picture, perhaps with cotton or string, which can be removed later.

Maybe the pictures really are level, but their subject matter creates the illusion that they are crooked.