The purpose of Orphan Rock

You can find the solution on the back of the claw: open your inventory, inspect it, and rotate it around. As you noted, the solution is:

• Outer: Bear
• Middle: Whale
• Inner: Snake

There are a few puzzles that consist of looking at the quest item at different angles: Bethesda seems to have been very proud of this feature, and these quests appear to just be a means to highlight it.

On the body of the person you mentioned, there should've been a book that mentioned Folgunthur. That's where you need to go to get the ivory claw: you can find it near Solitude.

Once inside, you'll find a dead adventurer who has the claw on his person.