An acrolect is a register of a spoken language that is considered formal and high-style.
The term mesolect refers to a register or range of registers of spoken language whose character falls somewhere between the prestige of the acrolect and the informality of the basilect. Mesolectic speech, where it is distinguished from acrolectic speech, is often the most widely spoken form of a language, generally being used by lower and lower-middle classes. Within the context of Creole languages, mesolects only appear in instances of a post-Creole speech continuum wherein speakers code-switch between various mesolectal levels within the continuum depending on context.
In linguistics, a basilect is a dialect of speech that has diverged so far from the standard language that in essence it has become a different language. A basilect represents the opposite end of the scale of linguistic formality from an acrolect. In certain speech communities, a continuum exists between speakers of a Creole language and a related standard language. Basilects typically differ from the standard language in pronunciation, vocabulary, and grammar, and can often develop into different languages.
(Additional reading: West Indians and their language Chapters 1-4 )