You need PDO to connect with databases but I am not sure if shared hosting environments allow setting ‘extensions’ for hosted sites separately…
you can ask you provider if it is possible to enable somehow PDO (as native PDO will be faster than alternatives). I would start with that. If there is no possibility - try to use substitute: http://www.yiiframework.com/extension/phppdo/
This library emulates PDO with PHP wrappers for standard db connection functions. It is in fact not so bad and for Oracle db I would even recommend this one over native PDO_oci as PDO_oci is not stable…