You'll need to write some code, probably a custom web part, but the
easiest way to solve this would be to use the Microsoft Single Sign on
service that ships with MOSS. Using SSO you can easily store the Java
credentials in an encrypted database and retrieve them based on the
security context of the logged on user or their group membership. Then
you can programmatically submit those credentials in the background to
authenticate the user against the MicroStrategy environment.

Take a look at the following MSDN article for more info:

msdn2.microsoft.com/en-us/library/ms984587.aspx

As per my understanding, SSO in sharepoint  works, something like, what ever
credentials a user provides while accessing the sharepoint site are stored
inside the SSO database, same credential values are used to integrate the other
applications.

One layman question, in our intranet site, domain user who logged into the
machine can access the sharepoint site directly, without need to provide  any
credentials.

Can you please help  me how this works in this scenario.

You understanding of SSO is not quite right. When you setup SSO you
define one or more applications. Each application can have up to 5
fields for storing credentials. For example, a traditional NT login
would be 3 fields (username, password, domain). Those 1-5 fields can
then be filled in either by an administrator or programmatically on a
per user or per group basis. At runtime the user can automatically
retrieve the credentials and use them to programmatically login to a
backend system. The only problem is that SSO does NOT include
anything out of the box for storing the credentials in SSO. You either
need to do that by writing a program or by using the administrative
interface in Central Admin. It also doesn't have anything out of the
box to supply the credentials to a back end system. You also would have
to write that, usually in a custom web part that will use the data.

IE is passing credentials from the workstation OS for Intranet users in
your environment. They are logged in, its just that IE can pickup the
credentials you used to login to the Domain and pass them in the
background to the server. Since you are logged in SSO will work
normally.