print_r is your friend for figuring out JSON structure.

<?php

$addresses = json_decode('{"addresses":{"address":[{"@array":"true","@id":"888888","@uri":"xyz","household":{"@id":"44444","@uri":"xyz"},"person":{"@id":"","@uri":""},"addressType":{"@id":"1","@uri":"xyz","name":"Primary"},"address1":"xyz","address2":null,"address3":null,"city":"xyz","postalCode":"111111"}]}}');

$_SESSION['address1'] = $addresses->addresses->address[0]->address1;
$_SESSION['address2'] = $addresses->addresses->address[0]->address2;
$_SESSION['address3'] = $addresses->addresses->address[0]->address3;
$_SESSION['city'] = $addresses->addresses->address[0]->city;
$_SESSION['postalCode'] = $addresses->addresses->address[0]->postalCode;

print_r($_SESSION);

Results in:

Array
(
    [address1] => xyz
    [address2] => 
    [address3] => 
    [city] => xyz
    [postalCode] => 111111
)

It can be done with json_decode(), be sure to set the second argument to true because you want an array rather than an object.

$array = json_decode($json, true); // decode json

Outputs:

Array
(
    [id] => 1
    [name] => foo
    [email] => [email protected]
)

This appears to work:

$url = 'http://www.worldweatheronline.com/feed/weather.ashx?q=schruns,austria&format=json&num_of_days=5&key=8f2d1ea151085304102710%22';
$content = file_get_contents($url);
$json = json_decode($content, true);

foreach($json['data']['weather'] as $item) {
    print $item['date'];
    print ' - ';
    print $item['weatherDesc'][0]['value'];
    print ' - ';
    print '<img src="' . $item['weatherIconUrl'][0]['value'] . '" border="0" alt="" />';
    print '<br>';
}

If you set the second parameter of json_decode to true, you get an array, so you cant use the -> syntax. I would also suggest you install the JSONview Firefox extension, so you can view generated json documents in a nice formatted tree view similiar to how Firefox displays XML structures. This makes things a lot easier.