In what year does Freak the Mighty take place?

The year that Freak the Mighty takes place is unknown.  As a reader, you could consider the date as "present day."  Eventually, that won't work with this book, but for now it does.  The cities and available technologies to Max and Freak are present day things.  The book simply can't take place long long ago, because the homes have basements with wood paneling, hospitals exist with surgery rooms, and the descriptions of schools ring true of modern day.  The book was published in 1993, and it makes sense for the author to place the time setting within an era that he is familiar with.  

There are moments in the book though that "go back in time."  Those are the times that Max and Freak travel via their imaginations to times that have dragons and all sorts of other fantastical creatures.