In the most general definition, a formal language is simply an arbitrary set of strings over a particular alphabet. Assuming the alphabet is nonempty, that means there will be infinitely many strings and thus uncountably many sets of strings. There are only countably many formal grammars, so many sets of strings (formal languages) are not definable by formal grammars.
Sometimes authors back away from the most general definition and require that the alphabet has to be countable or finite and the language has to be at least computably enumerable. In that case, you have to have a more specific definition of what a "formal grammar" is to make the question precise. Every c.e. language is generated by an "unrestricted grammar" in the sense of the Chomsky hierarchy, and every language generated by any grammar is c.e., so those classes of languages coincide. But, for example, not every c.e. language is a regular language in the sense of the Chomsky hierarchy.