Q. How do you adjust cooking time and temperature if you are cooking four casseroles in the oven at the same time? Also, what if you need to cook them at the same time, but one is to be at 350°F, one at 375°F, etc.?
There should be relatively little difference in the cooking time. It is your oven's job to keep the heat regulated at the set temperature. It may have to work harder initially when you place four cold dishes in the oven than if you only inserted one. But if the oven is preheated and you put the dishes in, it should crank up the heat quickly to maintain the set temperature. Theoretically, if each dish is surrounded by 350°F air, it will just take as long to cook as you'd expect, whether it is sharing the oven with other dishes or not.
The challenge though, is heating all four dishes evenly. With the oven packed, the hot air which is the heating medium circulates less freely, and your oven will have hot and cold spots. That's the reason you rotate pies and cakes and move the one on the top rack to the lower rack and vice-versa halfway through baking, so that each is more or less exposed to the same amount of heat for the same amount of time. Also, if the edges of two dishes are very close to one another, that seriously inhibits the flow of hot oven air to each dish, and those edges will take longer to cook.
In practical terms, it may take 10% to 15% longer to cook your dishes, and you're going to have to turn them and switch their positions once or twice. A convection oven, which uses a fan to circulate the hot air evenly throughout the cavity of the oven, solves these problems and makes it much easier to load up the oven and cook everything evenly.
Finally, in cooking terms, there's not much difference between 350°F and 375°F (175°C and 190°C). In fact, unless you've checked your oven's accuracy with an oven thermometer, it might routinely be off by 25°F. Both 350°F and 375°F are considered a "medium oven." Which you choose would only matter for the most delicate, heat-sensitive dishes, and if that's what you're cooking, you should rethink the four-dishes-in-the-oven-at-the-same-time plan.