I went to Activity->Revisions in the reputation panel, and I see 82 revisions but still no Strunk & White badge. Is there special considerations on the edit count? Is a revision an edit?
You need to have made edits to posts that are not your own, and only one edit per unique post counts.
You can see your progress by visiting the suggested edits statistics page, then hover over the progress bar at the top right:
to expand it to reveal a set of three more:
For the Strunk & White silver badge, look at the Copy Editor progress bar; you'll receive it when that indicates you've edited 80 posts.
Your revisions list on your profile counts multiple edits to the same post, as well as edits to your own, making it a poor indicator of your progress.