There are couple of links on BIRT page: http://wiki.eclipse.org/Integration_Examples_%28BIRT%29
Especially you should be interested in following ones:
- http://wiki.eclipse.org/Servlet_Example_%28BIRT%29_2.1 - servlet examples
- http://wiki.eclipse.org/Simple_Execute_%28BIRT%29_2.1 - running BIRT as Java application
- http://wiki.eclipse.org/Java_-_Dynamic_Report_Servlet_%28BIRT%29 - Dynamic report servlet
Let us know if that helps.