Need more space than a comment. @yorirou has the correct answer. However, to store/retrieve an array of strings each entered by different widgets, you have an easy path:
Wrap everything in a fieldset with the #tree property. All fields within that fieldset will be folded into an array structured based on the fieldset name for the variable name, and the individual field names for the key value. Array serialization is automatically handled on variable_get/set.
$form['custom_settings'] = array(
'#title' => t('My settings'),
'#type' => 'fieldset',
'#tree' => TRUE,
);
$form['custom_settings']['first_setting'] = array(
'#type' => 'textfield',
// etcetera
);
$form['custom_settings']['second_setting'] = array(
'#type' => 'textfield',
// etcetera
);
On output of the saved array, you would get something like this:
custom_settings = Array(
'first_setting' => 'some string',
'second_setting' => 'some other string',
)
You could get the same affect with a #validate handler, or using the #parents element in the forms arrays, but those would require extra work to wrangle the default value.