First off, you should really learn one and stick to it until you get a good grasp of it (trust me, I can't sit steady on one thing so I don't get much done).
Second off, there are many, MANY, coding languages to learn for each specific thing. Coding languages are almost as common as "real" languages. Each language can be general (such as c++), or very specific (such as css).
For the languages you want:
1. There are many different languages for websites, and many different ways to design one. To start you off, I recommend
this (html). Now, html isn't the only coding language for making a website. You can use CSS, PHP, XTML, Javascript (not to be confused with Java), and many others in conjunction with html. You can also use programs like
Adobe GoLive or
Dreamweaver. Now, to actually see any of this code you need a server, which you can find free ones
here. For an absolute beginner I reccomind freewebs.
2. Game coding can be very difficult, or very easy. Most of the easy ones are point and click type of "coding" based mostly on switches, such as
Rpg Maker. There is no standard language for games, but I think the majority are in C++ (I could be wrong). These are usually not for beginners, and if you try to start off with this, you will probably give up frustrated (unless your mind works the right way).
For flash games (most online games), you use
adobe flash. Flash is very simple if you learn it right, and you can also use it for animation (flash cartoons, such as those on newgrounds). I recommend learning html though, since that is a good foundation to build upon.