Can there be buffer overflow/overrun vulnerabilities in completely managed asp.net web portal.If yes how can this be tested.
In the general case, you don't need to worry about buffer overruns. This is one of the major advantages of managed code, garbage collection being perhaps the other major advantage.
There are a few edge cases that you should be aware of - any time your managed code interacts with unmanaged code (Win32 API calls, COM interop, P/Invoke, etc) there is a potential for buffer overruns in the unmanaged code, based on parameters passed in from managed code.
Also code marked as "unsafe" can directly manipulate memory addresses in such a way as to cause buffer overflow. Most C# code is written without using the "unsafe" keyword, though.