Here are some Oaxacan Food Specialties:
Alegria-sweet made with amaranth seeds and piloncillo
Almendrado de pollo-chicken in almond sauce
Asiento-Lard containing browned pork skin, often spread over toasted tortillas
Atole-thick corn based drink often flavored with chocolate, vanilla, nuts
Barbacoa-goat or lamb, grilled in pit, covered with avocado leaves
Champurado-atole made with chocolate
Chochoyotes-small masa dumplings
Clayodas (Tlayodos)-large dried tortillas spread with asiento
Enfrijoladas-folded tortillas with thick flavorful sauce of black beans, garlic, chile de arbol, and crushed dried avocado leaves
Heuvos Oaxaquenos-omelet like dish made with onions, served with chiles, garlic, and a tomato sauce flavored with serranos and epazote
Mezcal-distilled from smoked fermented heart of maguey plant
Moles
mole amarillo-yellow, made with regional chiles or quajillo, tomato, tomatillos
chichilo negro (black) made with burnt tortillas, avocado leaves, charred chiles chilhauacles
mole colorado (red) almonds, peanuts, spices, herbs, chocolate, anchos. often served with chicken
mole coloradito(light reddish brown) served with pork or chicken
mole manchamateles (deep red) "tablecloth stainer" made with pineapples,plantains, anchos, served with pork or chicken
mole negro(black) most common mole in Oaxaca, uses the chiles from Oaxaca
mole verde-tomatillos, epazote, herba santa, parsley, served with pork or chicken
Pipian-sauce like mole made of ground pumpkin seeds
Tamales Oaxaquenos-most common used mole negro as filling, but also have black beans as filling.
Well this is a start, drawn from some material from a group called Culinary Adventures, which does trips to Oaxaca.
I will look further for more ideas of what might be good to order.