When you specify insert="false" and update="false" in many-to-one element, you can include property element for the same column specified in many-to-one element. That means you have capability to set the value of application_id column using corresponding setter.
Code:
<?xml version="1.0"?> 
<!DOCTYPE hibernate-mapping PUBLIC "-//Hibernate/Hibernate Mapping DTD 3.0//EN" 
"http://hibernate.sourceforge.net/hibernate-mapping-3.0.dtd"> 
<hibernate-mapping package="hibernate"> 
<class name="Submissions" table="submission"> 
   <id name="submissionId" type="string" unsaved-value="null" > 
      <column name="submission_id" sql-type="raw(16)" not-null="true"/> 
   </id> 
   <property name="submissionNo"> 
      <column name="submission_no" sql-type="VARCHAR2(5)" not-null="true"/> 
   </property> 
   <property name="createdTs"> 
      <column name="created_ts" sql-type="Date" not-null="true"/> 
   </property> 
   <property name="lastModifiedTs"> 
      <column name="last_modified_ts" sql-type="Date" not-null="true"/> 
   </property> 
   ...... ....... ........ ...... ... 
   <property name="applicationId"> 
      <column name="application_id" sql-type="VARCHAR2(5)" not-null="true"/> 
   </property> 
   <many-to-one name="application" insert="false" update="false" class="Application" column="application_id" /> 
</class> 
</hibernate-mapping >
So now your code with slight modification is below
Code:
SessionFactory sessionFactory=HibernateFactory.buildsessionFactory(); 
Session session= sessionFactory.openSession(); 
Transaction tx=HibernateFactory.begintransaction(session); 
Submissions oSub=new Submissions(); 
// How will I set application id in Submission which has many-to-one relationship to application table 
oSub.setApplicationId( "007" ); // this sets the application id
oSub.setSubmissionNo("0005"); 
oSub.setCreatedTs(new java.util.Date()); 
oSub.setLastModifiedTs(new Date()); 
session.saveOrUpdate(oSub); 
HibernateFactory.commitTransaction(tx); 
System.out.println("Done"); 
HibernateFactory.close(session); 
Below code gives you an idea how to persist both Application and Submission at the same time with a call to saveOrUpdate.
Code:
SessionFactory sessionFactory=HibernateFactory.buildsessionFactory(); 
Session session= sessionFactory.openSession(); 
Transaction tx=HibernateFactory.begintransaction(session); 
Submissions oSub=new Submissions(); 
// How will I set application id in Submission which has many-to-one relationship to application table 
oSub.setApplicationId( "00001" ); // this sets the application id
oSub.setSubmissionNo("0005"); 
oSub.setCreatedTs(new java.util.Date()); 
oSub.setLastModifiedTs(new Date()); 
Application application1 = new Application();
// populate properties including appId
application1.getSubmissions().add( application1 );
oSub.setApplication( application1 );
Application application2 = new Application();
// populate properties including appId
application1.getSubmissions().add( application2 );
oSub.setApplication( application2 );
session.saveOrUpdate(oSub); 
HibernateFactory.commitTransaction(tx); 
System.out.println("Done"); 
HibernateFactory.close(session);