Instead of criminals, the enemy is germs, diseases and other vulnerabilities of the human body, tracked down like criminals. But House isn't just derived from Holmes. The character may also have influences from other mythic characters.
The stories usually follow the pattern of the scientific method: The team thinks up possibilities based on the evidence and then tests them, eliminating the ones that don't pass the tests until they come up with a theory that works. Or as Sherlock Holmes said, "When you have eliminated all which is impossible, then whatever remains, however improbable, must be the truth." Some critics have derided the plots for being formalistic, but if through interesting fiction, the writers are demonstrating how science works, there is genius in their method.