What is the style of the medley of Les Miserables?

By medley do you mean the end of act 1? The "One Day More" song?

If you do; its called a quodlibet:

A quodlibet is a piece of music combining several different melodies, usually popular tunes, in counterpoint and often a light-hearted, humorous manner. The term is Latin, meaning "whatever" or literally, "what pleases." There are three main types of quodlibet:

• A catalogue quodlibet consists of a free setting of catalogue poetry (usually humorous lists of loosely related items).
• In a successive quodlibet, one voice has short musical quotations and textual quotations while the other voices provide homophonic accompaniment.
• In a simultaneous quodlibet, two or more pre-existing melodies are combined.

"One Day More" falls into the last category: a simultaneous quodlibet.