Thor, manliest of manly men, macho superhero protector of Asgard, has to dress up as Freyja, most beautiful and feminine of all the goddesses, in order to get his hammer back. There's so much going on with gender here that we practically don't know where to start. Let's break it down:
First of all, the cross-dressing: As we mentioned in "Symbolism," Thor's cross-dressing in this story actually has the opposite effect of what you might expect. Instead of making Thor look like a sissy, it ends up confirming what a manly man he actually is, since he has so much trouble passing as a woman.
There's even more going on in the symbolic realm. Thor is the epitome of masculinity. We'd even go so far as to say that in Norse mythology, Thor's character represents ultimate masculinity. And Freyja is so associated with femininity that her name actually became the German word for woman: frau. So it's not just that Thor is transforming into Freyja. Man is transforming into woman. He can't really pull it off, which might signal this story's belief that maleness and femaleness are something natural to the person, something that you can't really take on and off like a costume.
On the other hand, though, there's another important cross-dresser in this story: Loki. Loki may be a guy, but he does a pretty darn good job at being a bridesmaid. He also uses the stereotype of the blushing bride succumbing to pre-wedding jitters to hoodwink Thrym into believing that Thor is really Freyja. Thrym's willingness to buy into this stereotype is his downfall. Maybe maleness and femaleness are natural to certain gods, while others can put gender on and off like a costume.
Now about that hammer. It's pretty clear that Thor's loss of his hammer is meant to be a symbolic of losing something else. Something else in his, uh, nether region. The forced cross-dressing is just the icing on the cake. Thor loses his manliness when he loses his ability to dominate others with his strength, signaling the story's connection of masculinity with physical power. Since he can't use his hammer, Thor has to use his brains. Does that mean the story connects brainy problem solving with femininity, contrasting it with "masculine" physical domination? It's certainly a possibility. If so, that might explain why Loki, who always takes an intellectual approach to problems, has no trouble passing as a woman.
Thor's usual approach to problems is to throw his hammer at them. In this particular story, though, the problem is that his hammer is missing. Without it, Thor has to use his brains to achieve his goals. This approach doesn't really come naturally to Thor. Cue Loki the trickster god, who uses cunning and cleverness all the time. It's thanks to Loki's quick thinking that Thor's crossing-dressing disguise lasts for as long as it does. He manages to convince Thrym that his bride's masculine appetite and fiery eyes are simply the result of pre-wedding jitters. Uh, right. Without Loki, we'd say that Thor would have about a 3% chance of tricking Thrym – and that's only because Thrym isn't too sharp.
"The Theft of Thor's Hammer" seems to be proving the necessity of a god like Loki, and the cunning and cleverness he represents. Sure, it's nice to have a beefy muscleman like Thor protecting Asgard, but muscle alone isn't enough. You've got to have some brainy people around when muscle falls down on the job. That makes all of us brains here at Shmoop feel pretty good about ourselves.