WordNet (r) 3.0 (2006):

eat up
    v 1: finish eating all the food on one's plate or on the table;
         "She polished off the remaining potatoes" [syn: eat up,
         finish, polish off]
    2: use up (resources or materials); "this car consumes a lot of
       gas"; "We exhausted our savings"; "They run through 20
       bottles of wine a week" [syn: consume, eat up, use up,
       eat, deplete, exhaust, run through, wipe out]
    3: enclose or envelop completely, as if by swallowing; "The huge
       waves swallowed the small boat and it sank shortly
       thereafter" [syn: immerse, swallow, swallow up, bury,
       eat up]

Moby Thesaurus II by Grady Ward, 1.0:

91 Moby Thesaurus words for "eat up":
   ablate, absorb, adore, and sinker, appreciate, assimilate, banquet,
   bask in, be a sucker, be pleased with, be taken in, bite,
   bleed white, bolt, burn up, consume, delight in, deplete,
   derive pleasure from, devour, digest, dispatch, dispose of,
   do justice to, down, drain, drain of resources, eat, eat heartily,
   enjoy, erode, exhaust, expend, fall for, feast, feast on, finish,
   finish off, freak out on, get away with, get down, get high on,
   gloat over, go for, gobble, gobble up, groove on, gulp down,
   impoverish, indulge in, ingest, lap up, like, line, love,
   luxuriate in, mop up, nibble, polish off, polish the platter,
   put away, put it away, regale, rejoice in, relish, revel in,
   riot in, savor, smack the lips, spend, squander, suck dry,
   surround, swallow, swallow anything, swallow hook, swallow up,
   swallow whole, swim in, swing at, take down, take in,
   take pleasure in, take the bait, tuck in, tumble for, use up,
   wallow in, waste away, wear away, wolf