To find words containing only the specified letters:
grep -v '[^aeiou]' wordlist
The above filters highlight lines in wordlistthat do not contain any characters other than those listed. This is a kind of use of double negativity to get what you want. Another way to do this:
grep '^[aeiou]+$' wordlist
which searches the entire string for a sequence of one or more selected letters.
, , , , , :
cat wordlist | grep a | grep e | grep i | grep o | grep u
(, cat , .)