According to the post - ELMAH for simple logging from the Elmah Google Groups:
ELMAH is not a general purpose logging facility so I would discourage using it such. It is designed and therefore best suited for logging unhandled exceptions. You can however use ELMAH together with a general purpose logger
There are many general purpose logger available, like NLog, log4net, Enterprise Library, Common Logging, etc. I would suggest you look into some of these as solutions for general purpose logging. Some of these provide bridges for Elmah that you may be able to leverage.