How can I 'or' 2 conditions using the api?
Barring some undocumented feature (which are rife in the API, so someone please correct me), I think you'll have to merge the two.  However, since you're dealing with "get" calls, it's straightforward to merge the two results.

First, you'll want to get rid of the sequential parameter; without it, you'll get arrays of values keyed by ID.  Then, you'll have a pretty simple situation:

$result = civicrm_api3('Contact', 'get', array(
  'birth_date' =&gt; array('IS NULL' =&gt; 1),
));

$result2 = civicrm_api3('Contact', 'get', array(
  'birth_date' =&gt; array('&lt;=' =&gt; "1960-01-01"),
));

$combined = array_merge($result['values'], $result2['values']);


The result will have only one row per contact.  Although obviously there's no overlap between people with no birth date and people with birth dates prior to 1960, you could use the same principle for merging potentially overlapping groups since the array key is the ID.