Because of the significance of Greek civilization in the development of engineering, mathematics, and science, names for Greek letters of the alphabet are widely employed in English to represent various constants, functions, and variables, though such use has extended to less technical contexts as well. Here’s a discussion of more casual usage.
Alpha and beta, the words for the first two letters of the Greek alphabet, were combined—in Greek, Latin, Middle English, and Modern English consecutively—to denote a set of letters, constituting a language’s written system, arranged in a traditional order. The first and last letters, alpha and omega, also have a resonance in Christianity, as the Bible has God referring to himself as “the beginning and the end, the first and the last.”
Alpha also has a sense borrowed from the use of the term in science to describe the first, primary, or dominant specimen in a group, as in referring to the leader of a wolf pack as the alpha. By extension, in popular culture, an alpha male is a dominant, competitive, and aggressive man. Alpha is also the first stage in development of a product, especially software or hardware, during which the bugs are (ostensibly) worked out.
Beta, in turn, refers to the next iteration of a product when a select group of people not involved in development of the product are invited to test it to enable further refinement. The word is also used in rock climbing as slang for “advice,” but this usage apparently stems from the name of the obsolete Betamax videotape format, not directly from the name of the second letter of the Greek alphabet.
Delta, based on the shape of the Greek letter by that name, came in English to refer to a triangular area of land where a river divides into smaller flows of water as it nears an ocean; numerous deltas exist around the world, but the most prominent are the Nile Delta, in Egypt, and (to Americans, at least) the Mississippi River Delta, in Louisiana—the latter not to be confused with the Mississippi Delta, a land-bound geographic region in the northern part of Mississippi. It is the latter designation, not the former one, that inspired the phrase “Delta blues” to refer to the distinctive music form that developed in that part of the United States.
Iota, as the smallest letter of the Greek alphabet, came to mean “a very small amount,” as in “He doesn’t have an iota of common sense.” The word was sometimes transcribed by Latin scholars as jota, which led to the synonym jot. (This is also the source of the verb jot, meaning “quickly make a note.”).
Omega, as mentioned before, refers to the last or least of anything, including the omega wolf in a pack, while psi, in addition to its frequent use in scientific and technical contexts, refers to psychic or paranormal activity.