The eels and kraken can pull you into the water, which can drown you very quickly unless you have magical breathing or are wearing a noncursed greased cloak or an oilskin cloak, in which case they cannot grab you.
Some people use the NetHack options file to replace the ; character with another, more readable one (such as 7) as a way to better distinguish a dangerous class of monsters from the water symbol.
Being on land scares sea monsters, and their HP constantly decreases; this will not kill them. This can make fighting them out of the water easier, however this might not always be possible.
Because eels and kraken can drown even the healthiest of adventurers, they are best fought at a distance from the safety of land. Try to avoid standing in squares adjacent to the water so that you cannot be grabbed.
The most resource-efficient ways to dispatch sea monsters are polearms and attack spells. Polearms allow you to fight at a distance without expending any resources, but targeting can be tedious if your proficiency with polearms is less than Skilled. Attack spells can be similarly effective so long as you have enough Energy to take out your foe.
Using projectile weapons is a less attractive tactic because the projectiles will end up falling in the water, becoming difficult to retrieve. Throwing daggers at sea monsters is highly inadvisable for this reason, but note that rocks can be substituted as expendable and readily available missile-weapons, with or without the use of a sling. However, with 3.6.1, be aware that thrown rocks can now skip across the surface of the water, increasing the chances of missing your target.
Another tactic is to carry an escape item and to melee them. On those occasions when an eel can successfully swing itself around you, you have one guaranteed turn to teleport it away or to engrave a single Elbereth into the ground with an athame, wand of fire, lightning, or digging. However, you should make sure you are not impaired to ensure 100% success. If you are levitating using a form of levitation that you can remove in one turn (ring, blessed potion, skilled spell, but not boots), you can also stop levitating and the eel will release you. (Obviously, stay over land if that is your plan for escape.)
If you are going to be drowned the next turn, taming the monster drowning you (with a scroll or the spell) might be helpful as the monsters which most commonly drown players all have a base MR of 0. Taming has no chance of missing, unlike a wand of death. For couatls, other strategies are preferable since they have a base MR of 30.
In small bodies of water (the Wizard's tower for example) it's possible to freeze the water with a wand of cold or cone of cold and attack it safely in melee if the cold attack didn't already kill it.
Finally, simply running away is also a viable strategy, especially on the Plane of Water.
- mon.c in NetHack 3.4.3, line 478: "but eels have a difficult time outside" [the water]