Almost everyone I know, or have known, calls it, 'soda.' As in, "Would you like a soda with that?" Then you get into what kind.
Unless you know the person well enough to know what they drink, then you ask them if they'd like, say, a rootbeer with that, or, by brand. Such as, Crush. Then if they say yes, you ask which kind.
I've heard people call it soda pop, or pop, but generally they are transplants, or they picked it up from relatives who are from somewhere else.
I also did meet someone who called all soda's cokes, and yes, she was from the south.
Here, however, if you ask for Coke, you will get a Coca Cola.
If the brand is unimportant, some people will just ask for a Cola, but it's still got to be that.
The fizzy clear stuff with minerals in it, or not, is either called, 'Mineral Water' or 'Soda Water.' I refer to it as the brand I drink, at home. If I was out and asking, I'd ask for a, mineral water. If I am talking to someone about it casually, I usually call it, soda water. 
The white powder for baking is called, Baking Soda, to differentiate from Baking Powder.
That looks complicated, but it's really not. We just call it what it is, or call it generically, soda.