你可以做算术和条件聚合：

select 
    max(case when mod(lvl, 2) = 0 then periods end) start_date,
    max(case when mod(lvl, 2) = 1 then periods end) end_date
from (
    select 
        regexp_substr (:p, '[^|]+', 1, level) as periods,
        level - 1 as lvl
    from dual
    connect by  level <= length (regexp_replace(:p, '[^|]+'))
) t
group by trunc(lvl / 2)

db小提琴演示：

START_DATE | END_DATE  
:--------- | :---------
2020/04/26 | 2020/05/02
2020/05/03 | 2020/05/10

如果您有一个或多个输入行，则该解决方案将起作用（而如果您向分层查询输入了多行数据，则分层查询将生成指数级增加的重复行数）。
将日期对转换为xml，然后使用 XMLTABLE 要转换：

SELECT id,
       x.*
FROM   test_data t
       CROSS JOIN
       XMLTABLE(
         ( LTRIM(
             REGEXP_REPLACE(
               t.value,
               '\|(\d{4}/\d{2}/\d{2})\|(\d{4}/\d{2}/\d{2})',
               ',<row><start>\1</start><end>\2</end></row>'
             ),
             ','
           )
         )
         COLUMNS
           start_date DATE PATH '/row/start',
           end_date   DATE PATH '/row/end'
       ) x

因此，对于您的测试数据：

CREATE TABLE test_data ( id, value ) AS
SELECT 1, '|2020/04/26|2020/05/02|2020/05/03|2020/05/10' FROM DUAL UNION ALL
SELECT 2, '|2020/06/01|2020/06/02' FROM DUAL

这将输出：

ID | START_DATE | END_DATE 
-: | :--------- | :--------
 1 | 26-APR-20  | 02-MAY-20
 1 | 03-MAY-20  | 10-MAY-20
 2 | 01-JUN-20  | 02-JUN-20

db<>在这里摆弄
或者，如果只有一个输入，则可以成对拆分数据：

SELECT REGEXP_SUBSTR ( :p, '\|(\d{4}/\d{2}/\d{2})\|(\d{4}/\d{2}/\d{2})', 1, level, NULL, 1 ) as start_date,
       REGEXP_SUBSTR ( :p, '\|(\d{4}/\d{2}/\d{2})\|(\d{4}/\d{2}/\d{2})', 1, level, NULL, 2 ) as end_date
FROM   DUAL
CONNECT BY LEVEL <= REGEXP_COUNT( :p, '\|(\d{4}/\d{2}/\d{2})\|(\d{4}/\d{2}/\d{2})' )

输出：

START_DATE | END_DATE  
:--------- | :---------
2020/04/26 | 2020/05/02
2020/05/03 | 2020/05/10

db<>在这里摆弄
或使用：

SELECT *
FROM   XMLTABLE(
         ( LTRIM(
             REGEXP_REPLACE(
               :p,
               '\|(\d{4}/\d{2}/\d{2})\|(\d{4}/\d{2}/\d{2})',
               ',<row><start>\1</start><end>\2</end></row>'
             ),
             ','
           )
         )
         COLUMNS
           start_date DATE PATH '/row/start',
           end_date   DATE PATH '/row/end'
       )

db<>在这里摆弄