Stan sure loves his vodka. Behind tea and kvas (a non-alcoholic beer), vodka (водка) is the most popular drink in Russia, but if you're old enough to read this, you probably know this already. Russian soldiers often drank small to moderate amounts of vodka before going into battle as it's believed to sharpen reflexes and make consumers more alert. Granted, drinking too much will likely give you a much bigger headache than nearly any other type of hard liquor can do. Vodka is one of Russia's main exports and is produced in unparalleled quantities. It's made from potatoes, which grow well underground in Russia's cold climate.
Kyle's green hat is an ushanka (ушанка), which is Russian for "earflaps." Having said this, his trademark headwear isn't very recognizable as such considering many Russians depicted in movies, television, photos, etc. are wearing their ushankas with the flaps up and secured to the top of the hat. And let's not forget the KGB-era red star and laurel from the Soviet era!
Kenny's redneck family must love the AK-47. The Russian selective-fire assault rifle also known as the Kalashnikov (Калашников) is popular with gun aficionados around the world and was produced in higher numbers than almost all other assault rifles combined. It quickly became a Soviet icon - a mechanical relic during a period of shoddy craftsmanship and poor quality control often synonymous with Russia and other former countries of the Soviet Union.
Cartman is a set of matryoshka (матрёшка) dolls, often called "babushka dolls" or "Russian nesting dolls." These decorative trinkets, often made of wood, usually depict a woman in traditional clothing, with identical or similarly-designed dolls placed inside, ranging in size. In more recent times, matryoshka dolls have been made of Soviet leaders, celebrities, religious characters, cartoon characters, or fairy tale characters.