If a cop smells weed or sees drugs in a car on a traffic stop, can he search my car, my person, my belongings?
Yes, if police officer smells drugs (or sees them) during an otherwise legal stop, the officer can then search your car and you for the drugs.
The general rule is that a warrant is needed for a search. That is one of the core protections against police and governmental abuses found in the U.S. Constitution and therefore applicable everywhere in this country. But like any rule, there are exceptions. One of those exceptions comes into play when, during a legal traffic stop, the police smell or otherwise have evidence of drugs.
While the warrant requirement is there to shield citizens, the courts have crafted a number of exceptions to it designed to prevent it from being a "sword" used by criminals to foil prosecution. One of those exceptions is the "exigent circumstances" exceptions. This states that if a warrantless search is necessary to preserve evidence or contraband which the police are aware exists but which would be lost, destroyed, hidden, etc. in the time required to get a warrant, the police may search without one. Another exception is the "plain sight" exception, which states that if the police perceive with their own senses criminal contraband or evidence, they may seize it, even if that means going into someone's home or car without a warrant. And while this second exception is called the plain "sight" exception, it really should be called the "plainly sensed" exception, since the police may rely on their noses as well as their eyes.
Here's how these exceptions play out when, during a legal traffic stop, the police smell marijuana:
(1) Because the police are allowed to act based on the evidence of their own senses, they can rely on what they smell to justify seizing any marijuana in the car or on your person (or in your luggage/bags, etc.).
(2) Because cars are, by definition mobile, and because the police cannot hold you indefinitely on a traffic stop, if they needed to get a warrant, you would drive away and dispose of the drugs long before they obtained one. The "exigent circumstances" require them to conduct warrantless search on the spot, to prevent the destruction or removal and hiding or drugs which they know, thanks to "plainly sensing" them, must be there.
So, while the police could not search just on a "hunch"--e.g., thinking for some reason that you "probably" have drugs--if they, in fact, smell drugs (e.g., if they saw any evidence of drugs, like the remnants of smoked "joints" or a "pot pipe"), they are allowed to search to find the evidence.
There is even a third exception which may come into play. In some circumstances, police may search to protect the public, as for example, if there is reason to suspect a bomb somewhere.
Since driving under the influence is not just a crime but can also be dangerous, the police could search to see if you are in fact driving while using drugs.