Vodka tonic tastes like bubbly slightly sweet lime water. It is a tad bitter at times, but very smooth going down the throat. If good vodka is used all you can taste is the tonic water. That's because vodka by law is a neutral spirit, meaning that it can have no discernible taste.
It depends on the recipe and the proportion of ingredients in it. Some can be sweet, bitter, sour, spicy, or savory, or a combination.
For starters, a true martini uses gin, not vodka.Beyond that, it is up to the bartender or whoever as to what kind of vodka you use for a vodka martini. That said, plain vodka appears to be most common.
I would recommend using this recipe to try making a vodka martini, http://www.foodnetwork.com/recipes/the-cookworks/the-classic-vodka-martini-recipe/index.html.
gin
It is a gin or vodka martini made with no vermouth
He drinks a vodka martini "shaken, not stirred."
A vodka martini is often made with 2 parts vodka to 1 part vermouth so 1 1/2 oz vodka and 3/4 oz vermouth.
Vodka Martini (shaken, not stirred) and in recent films, the Vespa Martini
A vodka martini
Martini's
Vodka Martini (shaken, not stirred) and in recent films, the Vespa Martini
Black Star Liner
There are bartender receipe books that you can find on ebay or amazon or even barnes and nobles that would have many drink receipes including vodka martini.