$ awk -v date="Feb 19" '{if($0~date){print;getline;print}}' o.txt
Feb 19, 2012 5:05:00 PM org.apache.coyote.http11.Http11Protocol init
 INFO: Initializing Coyote HTTP/1.1 on http-8080
 Feb 19, 2012 5:05:00 PM org.apache.catalina.startup.Catalina load
 INFO: Initialization processed in 771 ms

$ awk -v date="Feb 20" '{if($0~date){print;getline;print}}' o.txt
 Feb 20, 2012 5:05:00 PM org.apache.catalina.core.StandardService start
 INFO: Starting service Catalina
 Feb 20, 2012 5:05:00 PM org.apache.catalina.core.StandardEngine start
 INFO: Starting Servlet Engine: Apache Tomcat/6.0.29
 Feb 20, 2012 5:05:00 PM org.apache.catalina.startup.HostConfig deployDescriptor
 INFO: Deploying configuration descriptor test.xml

$ awk -v date="Feb 24" '{if($0~date){print;getline;print}}' o.txt
 Feb 24, 2012 5:05:01 PM org.springframework.web.context.ContextLoader initWebApplicationContext
 INFO: Root WebApplicationContext: initialization started
 Feb 24, 2012 5:05:01 PM org.springframework.context.support.AbstractApplicationContext prepareRefresh
 INFO: Refreshing org.springframework.web.context.support.XmlWebApplicationContext@5e4be2cc: display name 
 Feb 24, 2012 5:05:01 PM org.springframework.beans.factory.xml.XmlBeanDefinitionReader loadBeanDefinitions
 INFO: Loading XML bean definitions from ServletContext resource [/WEB-INF/applicationContext.xml]
 Feb 24, 2012 5:05:02 PM org.springframework.context.support.AbstractApplicationContext obtainFreshBeanFactory
 INFO: Bean factory for application context