Formatting data does not seem to work ..

You've your original data as *text, so you can do (I assume your data start in A1) in B1: =A1*1, than change cell format to mmm-yy or any other if you want

* - aligned to the left in cell

or

select entire column with your data
from the ribbon DATA >>> Text to columns and from new window: Finish.
Adjust format if necessary

Agree your data is probably text - test with =ISNUMBER(cell-ref) FALSE indicates text and it will need to be converted.

Another way to convert would be to highlight the entire range (not 100% sure this will work with time included, but worth a shot),
go to text2Columns
click Next/Next
click Date
select MDY
Finish

Then try your formatting again

@ Sandy, yup that is a very handly trick

Date is not text, it is a number. I would think that the date was pulled in from another program?

You are welcome

read my "dancing" footnote, here or above