tuck in: (informal) eat eagerly, with enjoyment.
When the guests arrived, Peter was already at the table tucking in.

lick: eat something by rubbing it with the tongue.
The boy was sitting in the garden licking an icecream.

have a snack: eat a small meal between the main meals.
She usually has a snack for lunch and then a larger meal for dinner.

stuff/gorge oneself: (informal) eat so much that one can't eat anything else.
He didn't want any meal because he had stuffed himself with bread and butter.

overeat: eat more than is necessary or healthy.
If you want to lose weight, you shouldn't overeat.

pig out: (informal) eat more than is necessary or healthy.
When she's depressed she always pigs out on chocolates.

make a pig of oneself: (informal) eat too much.
She made a pig of herself, she had the whole pizza for herself!

guzzle: (informal) eat or drink a lot, with greed.
You guzzled my dessert! What a pig!

bolt: eat quickly, because one is in a hurry.
He bolted down the burger in just a minute!

wolf down: (informal) eat quickly, because you are hungry or in a hurry.
He wolfed down his lunch but was still hungry.

gobble (up): eat quickly.
You shouldn't gobble your food.

scoff: (informal) eat quickly.
William scoffed all the cake before we could get any.

polish off: finish a meal quickly or easily.
I was so hungry I polished off all the food.

nibble: eat small amounts of food, by taking small bites.
You have to nibble sweet corn.

peck: eat sparingly, without enthusiasm, because you are not interested or not hungry.
Sally didn't like the fish. She only pecked at it.

chew: masticate, bite food several times before swallowing it.
The meat was so tough that it took a lot of chewing.

gnaw: keep biting something hard.
I watched my dog gnawing at the large bone.

chomp: eat, chew forcefully.
Francis chomped away at the meat.

munch: chew, eat noisily.
We all munched at the cookies as we watched the movie.

consume: eat or drink.
Are you going to consume all the beef?

sip: drink something slowly.
She was sitting at the table sipping her wine with pleasure.

suck (up): drink something with a straw.
Sally sucked up all the juice from the carton.

swig (back): drink quickly, gulp.
The thirsty man swigged back the water.

knock back: drink quickly.
Francis knocked back his beer in a flash!

quaff: drink a lot of something quickly, knock back.
Guests quaffed champagne while waiting for the bride to arrive.

gulp (down): swallow quickly.
Francis gulped down his beer quicker than anybody else.