Here you go:
public static void main(String[] args) throws ParseException {
SimpleDateFormat sdf = new SimpleDateFormat("MM/dd/yyyy");
String oeStartDateStr = "04/01/";
String oeEndDateStr = "11/14/";
Calendar cal = Calendar.getInstance();
Integer year = cal.get(Calendar.YEAR);
oeStartDateStr = oeStartDateStr.concat(year.toString());
oeEndDateStr = oeEndDateStr.concat(year.toString());
Date startDate = sdf.parse(oeStartDateStr);
Date endDate = sdf.parse(oeEndDateStr);
Date d = new Date();
String currDt = sdf.format(d);
if((d.after(startDate) && (d.before(endDate))) || (currDt.equals(sdf.format(startDate)) ||currDt.equals(sdf.format(endDate)))){
System.out.println("Date is between 1st april to 14th nov...");
}
else{
System.out.println("Date is not between 1st april to 14th nov...");
}
}