All definitions are taken from Webster's Encyclopedic Unabridged Dictionary of the English Language, unless otherwise specified.

Mermaid or Sea-maid (mur-mad)
An imaginary female marine creature, having the head, torso, and arms of a woman and the tail of a fish.

Merman (mur-man)
An imaginary male marine creature having the head, torso, and arms of a man and the tail of a fish.

Naiad (nay-ad) Classical Mythology
Any of a class of nymphs presiding over rivers and springs.
From Bullfinch's Mythology: The Naiades presided over rivers, streams, brooks, springs, fountains, lakes, ponds, wells, and marshes. They were divided into various subclasses: Crinaeae (fountains), Pegaeae (springs), Eleionomae (marshes), Potameides (rivers), and Limnades or Limnatides (lakes). Roman sources even assigned custody of the rivers of Hades to Naiades classified as Nymphae Infernae Paludis or the Avernales. For more about other kinds of nymphs.

Nereid (ner-e-id) Classical Mythology
Any of the 50 daughters of Nereus (Son of Pontus and Gaea); A sea nymph.

Oceanid (Osh-e-an-id) Classical Mythology
Any of the daughters of Oceanus and Tethys; a sea nymph.

Triton (tri-ton)
1. A son of Poseidon and Amphitrite, represented as having the head and trunk of a man and the tail of a fish, and as using a conch-shell trumpet.
2. Any of a number of minor sea-deities attendant upon the major sea gods.

Selkie (sel-ki)
Not in Dictionary. An Irish marine creature, having the skin of a seal, and the body of a human when the skin is removed.

Siren (si-ren) Classical Mythology
One of several sea nymphs, part woman and part bird, supposed to lure mariners to destruction by their seductive singing.

Undine (un-deen)
One of a group of female water spirits. According to Paracelsus, when an undine married a mortal and bore a child, she received a soul. For more about Paracelsus and his theories on the dwellers of the elements.