The sound you can hear is "uh", not "eh".
It is the French schwa and in this sentence, since the usual sound of "homme" ends with an M sound and "mange" starts with an M sound as well, the schwa is quite useful.
"Porc" and "pork" are both uncountable. Before an uncountable noun, with the meaning of "an unknown amount of a mass", "some" is optional in English but the partitive articles "du (masc), de la (fem) and de l' (before a vowel sound)" are required.
"Porc" is masculine, so you need "du porc".