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A "saga" is technically a term used to describe a long story originating from Nordic or Germanic countries. It does not refer to the number of books. It's just a long story. It was usually one book. Nowadays, it refers to a work of non-realistic "epic" work of fiction in the Nordic countries. So for example, the fairy tales and such were referred to as folksaga. Even though they are quite short.
So a "saga" does not refer to how many books there are, though in English, we almost exclusively use the term to talk about series, because "saga" has to be epic, and series tend to be more epic then single novels. A saga does refer to the genre- sagas are pretty much exclusively speculative fiction (fantasy and sci fi, though fantasy is more often referred to as a saga).
As for series, series is a generic term used to refer to any number of related books. So the Hunger Games is a series (3 books), as is the Women of the Otherworld (12 books so far). More often, series is used when it is uncertain how many books there will be, or if there are a very large amount of books.
If you want to refer to a book series by how many books there will be, the names are:
1 book (a/n: other authors prefer it to call 'stand alone novel') - Just a book
2- Duology or Dilogy
3- Trilogy
4- Tetralogy or quadrilogy
5- pentalogy
6- Hexology
7- Heptalogy or Septet
8- Octology
9- Ennealogy
10- Decology
However, most of those are uncommon. Trilogy is often used, Octology and Ennealogy are pretty much never used, and the others are usually only usedto refer to series by literary reviewers and the like, rather then common use.
Another term that is often used to describe a series is a Cycle, which is when a group of books focus on a general group of characters, but don't necessarily focus on one overarching plot line and may change protagonists on a fairly regular basis between books. A strange example of this would be Tamora Pierce's series: she has 3 tetralogies, a duology, and a trilogy which all focus on a different main character, but all together can be considered the Tortall Cycle, because they all fit in the same made up universe and share characters. In general, a Cycle is usually fantasy, sci fi, or historical fiction.
