I would say quickly switch to a twenty series WP theme to test.
If the issue still exists then there might be something going on with your WordPress install and you might want to try contact your host or re-installing it.
The posts mainly seem to be in order. The posts which are out of order are “sticky” posts, meaning they’ll stay at the top of the list regardless of their date.
If you remove the option to make them sticky, everything should go back to normal.