So, I'm staying in a location that has a gas oven with no discernable thermostat, and there are no thermometers in sight (oven, meat, or otherwise). The situation is such that I can't just run out and buy an oven or meat thermometer, and I'm not sure what to do. The people that I'm staying with have requested that I prepare a "traditional american christmas/thanksgiving dinner" (at least to the extent possible given the ingredients on hand and the circumstances). I have a turkey and several side dishes to prepare, and need advice on how to proceed. Any help is much appreciated.
It sounds like there is only one temperature that you can be absolutely sure of.... that water boils at the local boiling point. Since you haven't mentioned high altitude cooking, I am going to assume that is close to 212 F / 100 C. You also haven't said what sides you want to make so I am going to assume the traditional US type ones...
So things like mashed potatoes might be good, since you can boil them. Similarly, with vegetables.
The turkey is the toughest part, since you have strong constraints:
The best approach I can think of is to do a braised turkey recipe. The braising liquid will mitigate the unreliable heat of the oven if it is too hot; if the braise isn't bubbling slowly, you will know it is too low.
Braised dishes, by their nature are thoroughly cooked and should be quite safe.
You will find multiple recipes by googling "braised turkey recipe".
Root vegetables can be roasted at a wide, wide range of temperatures, and tested for being done based on softening. The risk is you won't know how long it will take. So you might precook them, and just reheat them for service, so that you aren't as time critical.
Cranberry sauce as a side is easy, and can be done stovetop without a thermometer.
The people who live there probably know how to work the oven. Ask them to set it up for baking a cake or a pie. That will probably be somewhere around 350-400. Close enough. Allow about 4 hours to cook the turkey. About 30 min before it's done, put in potatoes, parsnips, onions etc cut up to roast. Then take the bird out after 30 min and turn the oven up a little bit. You're hoping to hit 425, to crisp the veggies. While the bird rests, make the gravy and the cranberry sauce. If you're feeling super showoff, steam some brussels sprouts or green beans.
If the people who live there don't know how to work the oven, and you have time to experiment, figure out what settings you need to get a potato cooked but not crispy in 30 minutes. That's the temperature you want to use for the bulk of it.