as for relevance, MATCH AGAINST is capable of that, but probably not in the way you want.
matching similar strings, I don't think there is an easy way, but you might look into mysql regex.
if you e.g. want 'a' and 'ä' and 'ae' always be treated the same, and 'ss' and 's' and 'z', it should be possible to convert your keyword and use it something like:
SELECT * FROM table WHERE column REGEXP 'G(a|ä|ae)u(ss|s|z)$';