BEGIN
   FOR single_row IN (
      SELECT *
      FROM MY_TABLE)
   LOOP
      --iterate through columns of 'single_row'
      --for each nullable column do insert with real current column name and column value)
      --I assume each column is nullable except of ID
      INSERT INTO ANOTHER_TABLE VALUES (single_row.id, column_name, column_value);
   END LOOP;
END;

ID|ABC1|DA23|EE123|...
1|123|456|789|...
2|321|654|987|...

MY_TABLE_ID|COLUMN_NAME|COLUMN_VALUE
1|ABC1|123
1|DA23|456
1|EE123|789
... other columns from row 1
2|ABC1|321
2|DA23|654
2|EE123|987
... other columns from row 2