The script I'm using attaches session IDs to my site URLs. Does this affect the search engine readability of my site, and will it reduce the chance of my pages being indexed in the search engines? Is there any way to solve this?
You really should remove the session id from the url. There will be a setting either in your script or in php_ini which you can change.
Session IDs are can be problematic for the SEs and it can be a security risk as well. Try to remove them if posbile.
what script are you using? Is it custom or used regularly through the internet? If its been used by other people chances are theres a mod floating around for it somewhere already to remove them