mp and mf are mezzo-piano and mezzo-forte, respectively. Mezzo means "middle" or "medium", and so they're more towards the middle than piano and forte. So from softest to loudest, we have pp (pianissimo), p, mp, mf, f, and ff (fortissimo). More "p"s or "f"s are technically nonstandard, but are nevertheless used quite a lot.
sf or sfz is sforzando, a sudden emphasis. Literally, "straining".
rfz is rinforzando, and is more or less synonymous with sforzando for musical purposes. Literally, "reinforcing".
sfp is sforzando-piano, or sforzando followed immediately by piano. Slightly more dramatic than just fp. sfzp would be the same thing.
These abbreviations tend to get abused. You'll see things like sffz or sfffzp. These aren't proper abbreviations, the composer is simply adding more "f"s to mean more volume.