A few things come in mind

• have you checked nginx access/error log? Depending on your distro, log should be located at /var/log/nginx/access.log and /var/log/nginx/error.log.
• What role is your current WP user when uploading, does it have required capabilities ?
• Try to change wp-content permission to 755
• Are you having difficulties only with images file? If so, might be related to Imagick, try setting GD as default image editor. Add this next filter to default to GD in your functions.php. It will return GD before Imagick. The link provided is a plugin doing just that.

.

add_filter( \'wp_image_editors\', \'change_graphic_lib\' );

function change_graphic_lib($array) {
  return array( \'WP_Image_Editor_GD\', \'WP_Image_Editor_Imagick\' );
}