Is it weird to sell burgers and pizza in the same restaurant?

First, if you are doing a brisk business with your current mix of foods, don't change the mix of foods. If you feel you need to make your branding consistent with your menu, you could call your cuisine "America's Cravings" or some such. Since you are catering to travlers and truckers, you are not competing for diners looking for a particular ethnic cuisine, so you can stop worrying about that. What you need is for them to come in the door, or see your menu. I'd be inclined to name it something like Tina's. It's memorable, and lends itself to personal recommendation. Be certain that your takeout packaging lends itself to eating in a car. Boxed pizza and sandwiches have a built-in condiment shelf for fries, ketchup and such. You might also put together TOGO specials with burgers, hot dogs, pizza and fries for family sizes. Range the offerings (3 or 4, 5 or 6) and put together a "trucker's dream", a quart size drink of choice with a substantial sandwich or pizza, fries, and one additional snack per hour for the next 5 hours. Finally, continue testing new ideas. Run new items and combos for a month, and if they work and are profitable, add them to the menu. If they flop, that's the end of them.

BTW, I'm fond of fried fish, like the one Burger King used to sell but downsized.

Ni i think it is great

No, that's not weird - several places do that.

Not really. You can probably get away with other "American style" foods too

no it's very good and i am very happy becuse i love both food

That is the menu every pizza shop in my city has.

Just sell cheese burger pizzas (personal size) - the sauce ketchup and mustard spread thin, the cheese mild yellow cheddar mixed with mozz. Cook the hamburger with onions and top the pre-cooked pizza with the hamburger mix. After cooking add (By request) diced dill pickles, sliced/chopped lettuce and tomatoes.

Problem solved.

There is a truckstop restaurant, i believe in Texas, purportedly the largest one in the world, where you can buy anything from burger to pizza to sushi. A varied menu in a truckstop if not unusual at all. 

Not where I live. It is fine.

I've known takeaway shops to not have a main focus and do a few things, common around here are Chinese takeaways that also do pizza and burgers which are soooooo not Chinese but you should sell what is in demand.