Debating health is off topic here, but I think I can answer some of your question. Since you mentioned Chow Mein. I would start by saying that technically speaking you can NOT cook Chow Mein without oil. Chow directly translates to "fried" and Mein translates to "noodle". As frying (even stir/wok/pan frying in this case) by definition requires oil...
Now, can you cook noodles and sauce without oil? Sure, but it'd make a slightly different dish. You could boil the noodles for example, grill or steam the meat/vegetables and then mix it all together with sauce. You could still probably make a good dish this way. You won't get a typical chow mein though.
Chow mein aside, you could probably take a really good non stick or seasoned pan/wok and simply cook the meat/vegetables with a bit of water/broth. You'd essentially be lightly steaming it.
Though as an alternate suggestion, I would instead start with looking for dishes that utilised other cooking techniques, boiling, braising, steaming, grilling as examples. Also, can you use a, very, very small amount of oil? With the right pan a little bit goes a long way.
If you're eating meat/nuts/other things you'll get fat anyway though, some oils suitable for cooking are pretty good for you. I'd also, suggest talking to a doctor/nutritionist about how much oils are okay and which oils are okay. Not all fats are equal and humans need some fat to survive.