Why is orange juice or apple juice added in a smoothie?

Apple juice will give you very little additional taste, but it will sweeten your smoothie. Especially filtered apple juice has a rather subtle flavor which is easily covered by other fruit flavors. Juice producers use this to make their juices cheaper - if a juice advertises 100% fruit, and a flavor from an expensive, non-juicy fruit like strawberries, it is usually a blend of a small amount of strawberry juice and a large amount of apple juice (this is not fraud, the ingredients are listed on the package if you care to read it). Apple juice is normally made from low-acid apples, and it tastes quite sweet, so it is useful not only for bulking, but also for sweetening blends made with sour juices like elderberry, cranberry, etc. In a smoothie, it will have the same effect as in a juice blend, plus a diluting effect, as it is less viscous than your other ingredients. It won't amplify the flavor of the smoothie, it will even reduce it, as sugar tends to suppress other flavors in general. But the reduction won't be too big, and you might find the overall result better if you are accustomed to heavily sweetened food. You can also remove the sugar if you use apple juice - I wouldn't put it there anyway, even without juice.

Orange juice is much more acidic than apple juice, and it has a stronger aroma. It will add an orange flavor to your smoothie. I would count this as an advantage, because orange flavor goes especially well with bananas and is OK with strawberries too. It will also make the smoothie taste more sour, and again dilute it. Overall, the effect will be pleasant. As for what constitutes "overpowering" the taste, I think this is subjective. You should just experiment, adding a the juice in small proportions, until you have achieved the ratio which tastes good for you.

You need to add some kind of liquid to a smoothie to get the right consistency; otherwise it'll be too thick. Milk does that in your current recipe. Replacing the milk with juice would get you a more fruity, less milkshakey flavor to the drink (I prefer mine that way and use a variety of juices rather than soymilk). Juices tend to be sweet, so you won't need the extra white sugar.

If you use juices that don't taste too heavy (you know how orange juice can sometimes be super heavily flavored? Don't use those brands), you won't overpower the fruit before making the drink too diluted to really be called a smoothie. Apple juice is usually safer than orange if you're worried about it. I don't know how much milk you normally put, but assuming you like that ratio, try the same in apple juice -- I find ratio of liquid affects the consistency more strongly than the flavor.

There are a couple of "make your own Orange Julius" recipes online. I would suggest starting with that and work in your strawberries and bananas to your own taste.

If you reduce the quantity for frozen OJ concentrate (but not eliminate it) and then sub in the fresh fruit and perhaps sub in your yogurt for some of the milk you should get pretty close.

It find it adds a bit of taste from the OJ (yum!), but the main thing it does is add excess sugar to the drink. A cup of Orange juice can have over 20g of sugar!! (That's about 5 teaspoons)