You can use REGEXP:
SELECT field FROM table WHERE field REGEXP '(his$|^tha|nothe)'
However, regular expressions in MySQL are quite primitive, for example they will not work well with utf-8 character sets.
Postgresql has very good regular expression support and will work for utf-8 characters as well, so it is better suited for languages other than English or Latin in this case (however, much more limited in the choice of collations).