What type of lubricant should be used on oven door hinges?
Although they don't get as hot as the interior of the oven oven hinges are exposed to a significant amount of heat, so you should pick a lubricant which isn't going to burst into flames when exposed to heat, dry out, or gum up. My usual go-to oil for the home is 3 in 1 oil, but I wouldn't use it here because of the heat. 3 in 1 make a high performance spray lubricant which handles high temperatures, sprayon make a food-grade high temperature lubricant spray, and you can also get spray on bearing lube (for cars but is good for high temperature) - all of which would be fine for this application. 

I would recommend a spray on lube because oven hinges tend to be hard to access, and the spray will help force it in better, however if you gave good access you could get a tube instead.