Here is the complete warning:
Strict warning: Declaration of Zend_Gdata::import() should be compatible with Zend_Gdata_App::import($uri, $client = NULL, $className = 'Zend_Gdata...', $useObjectMapping = true) in include_once() (line 45 of /home/presbyte/public_html/droogle/sites/all/modules/Droogle/Zend/Gdata.php).

Is there any file in the Droogle folder that confirms the version of Zend required? I have the latest version: 1.12.3

also this in the logs:
Strict warning: Only variables should be passed by reference in droogle_show_docs() (line 246 of /home/presbyte/public_html/droogle/sites/all/modules/Droogle/droogle.module).

My host is running php5.4 if that helps. Here is the drush pmi output:

Extension : droogle
Project : Droogle
Type : module
Title : Droogle
Description : Babson developed module to interract with google apps.
Version : 7.x-2.0-beta10
Date : 2013-05-06
Package : Babson Development
Core : 7.x
PHP : 5.2.4
Status : enabled
Path : sites/all/modules/Droogle
Schema version : module has no schema
Files :
Requires : libraries
Required by : none