How do I change the delta values using a hook? I have a view getting all fields from nodes that have a relationship with the viewed node (using delta = all); it then only shows one node using CSS styles.

How do I change the delta value for every request and take its value as an argument from the URL?

I reloaded the page from JavaScript when the user needs to see the next field (using pager controls). 

Which hooks does the Views module provide to edit that value?
You can specify the validation criteria with PHP code in your contextual filter settings:

When the filter value IS in the URL or a default is provided

Specify validation criteria -> PHP Code

if($handler-&gt;argument){
  $view-&gt;display['default']-&gt;handler-&gt;options['pager']['options'] = array(
    'offset' =&gt; 0, 
    'items_per_page' =&gt; $handler-&gt;argument
  );
  return true;
}
else {
  return false;
}


That's it. Now, for every request the delta will be equal with the argument from the URL.
$handler-&gt;argument It's the argument which has been provided by your contextual filter.