WITH OPL AS (  
    Select *  
    FROM TBL_OPLAG  
       WHERE NR = '11'  
       AND OPL_DATE BETWEEN start_date AND end_date
      
    ,REK AS (  
    SELECT *  
    FROM REK  
       WHERE NR = '12'  
       AND REK_DATE BETWEEN start_date AND end_date  
      
    SELECT *  
    FROM OPL  
    JOIN REK ON OPL.OPL_DATE = REK.REK_DATE

orclz>
orclz> var v1 number
orclz> var v2 number
orclz> exec :v1:=2000

PL/SQL procedure successfully completed.

orclz> exec :v2:=4000

PL/SQL procedure successfully completed.

orclz> select * from emp where sal between :v1 and :v2;

     EMPNO ENAME      JOB              MGR HIREDATE                   SAL       COMM     DEPTNO
---------- ---------- --------- ---------- ------------------- ---------- ---------- ----------
      7566 JONES      MANAGER         7839 1981-04-02:00:00:00       2975                    20
      7698 BLAKE      MANAGER         7839 1981-05-01:00:00:00       2850                    30
      7782 CLARK      MANAGER         7839 1981-06-09:00:00:00       2450                    10
      7788 SCOTT      ANALYST         7566 1987-04-19:00:00:00       3000                    20
      7902 FORD       ANALYST         7566 1981-12-03:00:00:00       3000                    20

orclz>

CREATE TABLE DEV_SAURABH.TEST_T
(
  NR        VARCHAR2(20 CHAR),
  OPL_DATE  DATE,
  END_DATE  DATE
);


CREATE TABLE DEV_SAURABH.TEST_K
(
  NR        VARCHAR2(20 CHAR),
  OPL_DATE  DATE,
  REK_DATE  DATE
);


INSERT INTO test_t 
VALUES(
        '11'
       ,trunc(sysdate)
       ,trunc(sysdate)+2
      );

INSERT INTO test_t 
VALUES(  '12'
        ,trunc(sysdate)
        ,trunc(sysdate)+4
     );
    
INSERT INTO test_k 
VALUES(  '11'
        ,trunc(sysdate)+1
        ,trunc(sysdate)
      );
    
INSERT INTO test_t 
VALUES(   '12'
         ,trunc(sysdate)+3
         ,trunc(sysdate)
     );

Final Query: 
-----------

WITH OPL AS ( 
                    Select *  
                    FROM   test_t 
                       WHERE NR = '11'  
                       AND OPL_DATE BETWEEN trunc(sysdate) AND trunc(sysdate) + 1 
                 )     
    ,REK AS (  
                SELECT *  
                FROM   test_k 
                   WHERE NR = '12'  
                   AND REK_DATE BETWEEN trunc(sysdate) AND trunc(sysdate) + 4
          )      
    SELECT *  
    FROM OPL  
    JOIN REK ON OPL.OPL_DATE = REK.REK_DATE

SQL> define start_date=to_date('20150501 23:23:59','yyyymmdd hh24:MI:SS');
SQL> select &start_date from dual;
old   1: select &start_date from dual
new   1: select to_date('20150501 from dual
ERROR:
ORA-01756: quoted string not properly terminated


SQL> define start_date=23
SQL> select &start_date from dual;
old   1: select &start_date from dual
new   1: select 23 from dual

        23
----------
        23

SQL>

SQL> var x date
Usage: VAR[IABLE] [ <variable> [ NUMBER | CHAR | CHAR (n [CHAR|BYTE]) |
                    VARCHAR2 (n [CHAR|BYTE]) | NCHAR | NCHAR (n) |
                    NVARCHAR2 (n) | CLOB | NCLOB | BLOB | BFILE
                    REFCURSOR | BINARY_FLOAT | BINARY_DOUBLE ] ]

SQL> col val new_value val
SQL> select 1 val from dual;
       VAL
----------
         1

1 row selected.

SQL> def val
DEFINE VAL             =          1 (NUMBER)

SQL> define start_date=to_date('20150501 23:23:59','yyyymmdd hh24:MI:SS');
SQL> define start_date
DEFINE START_DATE      = "to_date('20150501" (CHAR)
SQL> define start_date="to_date('20150501 23:23:59','yyyymmdd hh24:MI:SS')";
SQL> define start_date
DEFINE START_DATE      = "to_date('20150501 23:23:59','yyyymmdd hh24:MI:SS')" (CHAR)
SQL>

define start_date="to_date('20150501 23:23:59','yyyymmdd hh24:MI:SS')";
select to_date(start_date)...

SQL> define start_date='to_date(''20150501 23:23:59'',''yyyymmdd hh24:MI:SS'')'
SQL> define start_date
DEFINE START_DATE      = "to_date('20150501 23:23:59','yyyymmdd hh24:MI:SS')" (CHAR)
SQL>

to_date('&start_date','yyyymmdd')