"Invalid relational operator" usually means that you have a where clause without a comparison. In your case, the where clause has the conversion to_date(), but no comparison. Perhaps you mean something like:
SELECT *
FROM WVT.WVCAS
WHERE dttmcutpull > sysdate - 1;
In other words, merely converting the data is not sufficient, you have to compare it to something.
If you just want to do the conversion, then put that in the select:
SELECT w.*,
to_char(dttmcutpull, 'mm/dd/yyyy hh24:mi:ss') as NewDate
FROM WVT.WVCAS w;
EDIT:
You have to convert each column independently, not all at once. to_char() takes two arguments, a date and a format:
SELECT w.*,
to_char(dttmcutpull, 'mm/dd/yyyy hh24:mi:ss') as date1,
to_char(DTTMPULLll, 'mm/dd/yyyy hh24:mi:ss') as date2,
to_char(DTTMRUNll, 'mm/dd/yyyy hh24:mi:ss') as date3,
to_char(SYSLOCKDATEll, 'mm/dd/yyyy hh24:mi:ss') as date4,
to_char(SYSMODATEll, 'mm/dd/yyyy hh24:mi:ss') as date5,
to_char(SYSCREATEDATE 'mm/dd/yyyy hh24:mi:ss') as NewDate
FROM WVT.WVCAS w;