Bologna is often spelled "baloney" which is how it is pronounced in AE.
Aside from a sometimes delicious and cheap sandwich meat, baloney also means preposterous lies or drivel.
"Full of it" is often a euphemism for "full of shit", which means full of preposterous lies or drivel. If we are speaking metaphorically, "eat it" could stand for "swallow it", which can mean "believe it".
So, my translation:
This is a preposterous lie. Believe it, and you'll be full of lies.