the army calls it a dineing facility or d-fac
the navy calls it a mess deck or hall
the air force calls it burger king

Don't know of any actual military lingo, but I've got some from Cadets.

Washroom:

Sea Cadets: Head
Army Cadets: Latrine
Air Cadets: Washroom
We Pilots: Place to go pee

Dining Hall:

Sea Cadets: Mess
Army Cadets: Mess
Air Cadets: Mess
We Pilots: Subway