Anguilliformes (eel) is prey of:
Pandion haliaetus
Anatidae
Phalacrocoracidae

Based on studies in:
USA: New York, Long Island (Marine)

This list may not be complete but is based on published studies.

Anguilliformes (eel) preys on:
detritus
Plantae
Ruppia
Decapoda
Fundulus heteroclitus
Actinopterygii
roach

Based on studies in:
USA: New York, Long Island (Marine)
USA: Rhode Island (Marine)
England, River Cam (River)

This list may not be complete but is based on published studies.

Energy-efficient long distance swimming: eel
 

Eels and lampreys swim long distances but conserve energy by using a lateral wriggle.

   
  "The most primitive and ancient method of locomotion among water dwellers was probably the lateral wriggle, whereby a wave travels from head to tail and increases in amplitude. Many primitive invertebrate swimmers use this kind of locomotion. In many aquatic animals (lampreys, eels), wriggling is aided by vertical stabilizer fins that extend the sides of the body and thus facilitate power transmission to the water. Cat sharks, some true sharks, lungfish, and sturgeon also swim with this lateral slithering motion. How efficient and energy-saving this method of locomotion is can best be seen by taking a look at the eels, which cover thousands of kilometers on their wanderings through the oceans. Slow-motion pictures of their movements disclose the principles of physics on which they are based. The essential prerequisite for getting ahead by wriggling through the water is for the body wave to travel rearward faster than the fish travels forward. The wriggling animal thereby exerts pressure on the water along the wave loops moving backward. While the laterally directed components cancel each other out over the entire fish, the forward- and backward-directed components add up to the propelling force." (Tributsch 1984:52)
  Learn more about this functional adaptation.