update tbl set columnA = columnB

create or replace function is_date (
      P_String in varchar2
    , P_Date_Format in varchar2
      ) return number is

   l_date date;

begin

   l_date := to_date(P_String, P_Date_Format);

   return 1;
exception when others then
   return 0;
end;

update my_table
   set date_column = to_date(char_column, 'yyyy-mm-dd')
 where is_date(char_column, 'yyyy-mm-dd') = 1

update my_table
   set date_column = case when is_date(char_column, 'yyyy-mm-dd') = 1
                               then to_date(char_column, 'yyyy-mm-dd')
                          when is_date(char_column, 'yyyymmdd') = 1
                               then to_date(char_column, 'yyyymmdd')
                          ...
                          snip
                          ...
                     end

UPDATE tbl
   SET columnA = DECODE(type, '1', DECODE(INSTR(columnB, '-'), 5, TO_DATE(columnB, 'YYYY-MM-DD'),
                                                                  TO_DATE(columnB, 'MM/DD/YYYY')),
                                   TO_DATE(columnB, 'MMDDYYYY'));