First: if you are given 7 letters, do you want all words of less-than-or-equal-to 7 letters, or just the 7 letter words? I'm guessing all.

The first thing to do is to canonicalize your dictionary by alphabetizing the words. For speed reasons, it would make sense to exclude any words longer than 7 letters, and to output the canonicalized dictionary into multiple files, based on word length. Each line would have the canonicalized version and then all the words that it represents.

The next thing to do is to generate all the subsets (the powerset) with two or more members, of the set of characters you've been given. Blanks have to be handled specially: given blank-and-six-letters, you'd generate the powerset of a-plus-those-six-letters, b-plus-those-six-letters, etc.

For each member of your powerset, search the appropriate file.

Of course, there's nothing Perl-specific about any of this.