Can this mean "I'm eating stew and pork" as in English, or only that I have them in my possession?
No, that would be Táim ag ithe x (I'm eating x).
Tá x agam means I have x, not I'm having x.
I don't know about irish, but Scottish Gaelic would use the verb "to take" in this sense, just like most other Western European languages do.
Irish uses caith in this way, to take (consume) food, drink, medicine, etc.
I tried "stew with pork", is that wrong?
"pork stew" is counted wrong. Pork stew seems more natural than separate stew and pork, but apparently Irish doesn't use this construction for that.
“Pork stew” would be stobhach muiceola, using the genitive of muiceoil (i.e. “stew of pork”).
Ham instead of pork no?
"Ham" is liamhás, though in Ireland you'd be more likely to bake a ham and boil bagún (not the same cut that Americans call "bacon").