The "|" also needs a backslash to get its special meaning.
echo "blia blib bou blf" | sed 's/bl\(ia\|f\)//g'
will do what you want.
As you know, if all else fails, read the manual :-).
Matches either REGEXP1 or REGEXP2.
Note the backslash...
Unfortunately, regex syntax is not really standardized... there are many variants, which differ among other things in which "special characters" need \ and which do not. In some it's even configurable or depends on switches (as in GNU
grep, which you can switch between three different regex dialects).