How can I stove-cook meals for groups of 6-8 with only one burner?

Generally, it is said that you should avoid pans which are not the same size as the burner. You are wasting energy in both the "smaller" and "bigger" case. Besides, as Jessica mentioned, you are wasting time and getting lower quality food with a larger pan, because you have to stir a lot, and still get unevenly heated food.

But if the alternative is to cook two batches in a fitting pan, I still think that you are saving electricity and time with the inefficient large pan. So I would stay with it.

I can also recommend buying more burners and an oven, if you are going to cook. A portable burner is very small and can be stuffed into a cabinet when not needed, to save counter space even in the tiniest kitchen. It can be cheap, or you can get an induction one for better quality heating and energy saving. A toaster oven is, in my experience, much more useful than a microwave. This will depend on the way you eat - if you frequently get frozen meals, the microwave is more convenient. I do all of my normal baking if a toaster oven, and it does everything, even complicated cakes, so if you are serious about cooking, it might be a better use of space than the mw.

Besides the recommendations for 'one pot meals' (stew, pot roast, chili, hearty soups, etc. ... which would require a deeper pot), as you also have the rice cooker, you may want to consider rice-based cuisines:

• Chinese (stir fries ... but don't crowd the pan; cook a vegetable or two at a time, then put it in large bowl to the side; cook the meat (possibly in a batch or two), make the sauce, then mix everything together in the bowl.)
• Cajun / Creole : étouffée, gumbo, red beans & rice.
• Japanese : donburi, curry rice, hayashi raisu, chirashi sushi
• Filipino : any stew (menudo, adobe, caldereta, puchero, afritada etc.) with garlic rice
• Thai : curries (massaman, rendang, etc), soups, etc.
• Indian: any dry or wet curry

Other things to consider:

• You can also use the burner & rice cooker together : sauté meat and vegetables, then add them to the rice cooker with rice and cook. This could work for dirty rice, jambalaya, charleston red rice & sausage, etc.
• You can add flavorings to the rice cooker so there's more variety each time (eg, tomato juice for red rice; tumeric, sauteed onions, cloves, cinnamon and cardamom for indian dishes; sofrito or salsa for mexican dishes.
• Not everything has to be cooked. There are plenty of dishes where only part of the dish is cooked, and then assembled. (spring rolls, bahn mi, taco, lettuce wraps, etc.; bonus points if you can get your guests to do the assembly)
• Most rice cookers can double as steamers. So you can steam some vegetables as a side to go with the main dish.
• Consider dishes that don't require any cooking. (cole slaw, marinated vegetables, etc.)
• Consider dishes that can be served at room temperature, (spanish tortilla, fritatta (although without an oven, you'll have to flip it), fried chicken) or even cold (eg, gazpacho, although it can be a lot of fine dicing if you don't have a blender)

You may also be able to cook something on the burner, put it into the rice cooker to stay warm, then cook another dish ... but I wouldn't try holding things that way for too long (and it may only work with fairly wet dishes; you might want to put a towel over it to help hold in the heat)

... and that's not even getting to the microwave. (to steam vegetables, heat water to soften rice noodles, warm up sauces that you made in advance (slowly at low power), anything you can make a day ahead of time and then warm up before serving (eg, most soups), etc.)

I see no reason a single burner stove should be an insurmountable obstacle to cooking a one-pot dish serving multiple people. It is ok if the pan is a little bigger than the burner. The main problem with a burner smaller than your pan is it may cause uneven heating, however, frequent stirring or rotation of food in the pan so everything is over the warmest part of the pan will help minimize that effect.

If you only have one hob then it sounds like you need proper pots. There are loads of meals you can make in just one pot. I am a 'do by instict' rather than 'do by measurement' cook so I am sorry that this is quite vague. Why not make a casserole? Par boil your vegetables (carrots, parsnips, leek...whatever you want). Drain veg and leave aside. Sauté onions and add meat. Once meat is cooked drain any excess fat and readd veg. Make enough gravy to cover meat and veg (you can choose your gravy depending on the meat you use). Add any necessary herbs and bring to the boil.