Can i bring teriyaki on an airplane? Or what food is allowed on an airplane?

..yes, you can bring food on the plane. whether you eat it or carry it for someone else its ok. the only exceptions i know of are: fermented food ( bacteria / pungent smell ). durian fruit ( very pungent smell, not allowed in most hotels either ). although some "countries" won't allow certain foods in. like in Dubai an indian chef was arrested on drug smuggling charges while transiting, for carrying poppy seeds ( technically its opium, although it has no narcotic effect...) i usually buy take away food from airports or on the way to airport since the food served on most flights tends to be small in quantity and bland. i also opt for burgers or steak sandwiches. but teriyaki sounds like a great and tasty option :) enjoy.

You don't specifically mention the US but I am figuring that is where you are taking about. Food itself is allowed, it just comes down to a courtesy issue with your fellow passengers for smells. The issue in this case is if there is Teriyaki sauce with(or on) the item. If it is lightly sauced you are probably okay. If there is enough sauce that it is pooling in the container, they may treat this as a liquid and subject to the 3-1-1 rule. Meaning that it must be in a container 3.4oz(100mL) or less and be placed separately in a quart sized zip top bag with the rest of your liquids. If they do treat it as a liquid and it is not packaged correctly they won't let you correct it, they will just confiscate the entire meal. I would suggest if you get this to have the restaurant put the item in the container "dry" and give you a separate container for the sauce(that does not exceed 3.4oz). I do have to correct the above person though. In MOST cases you can keep food in the "danger zone" of between 40 and 120 degrees Fahrenheit for about 4 hours. But personally that still makes it a bit too close for comfort in trying to avoid food poisoning.

Remember Bactria grows quickly on lukewarm foods- any longer than say 30 minutes not hot or cold and you are risking food poisoning- especially on chicken or pork