Is there a way to see the access log of a table?
You need to be granted the necessary permissions on the table that contains the audits.  The minimum for you to achieve what you want is you need to be granted SELECT on that table.

As far as check if something is being inserted/deleted, you could always create a trace with SQL Profiler.  At the same token though, you need ALTER TRACE permissions on the server, and if you don't have the former SELECT permission I doubt you have ALTER TRACE.